{\rtf1{\fonttbl{\f2 Times New Roman;}{\f3 Times New Roman;}{\f4 Times New Roman Bold;}{\f5 Times New Roman;}{\f6 Times New Roman Bold;}{\f7 Times New Roman Bold;}{\f8 Times New Roman;}{\f9 Times New Roman Italic;}{\f10 Times New Roman Bold Italic;}{\f11 Arial;}{\f12 Times New Roman;}{\f13 Times New Roman Bold;}{\f14 Times New Roman Bold;}{\f15 Times New Roman;}{\f16 Arial Italic;}{\f17 Times New Roman;}{\f1000000 Times New Roman;}}{\colortbl;\red0\green0\blue0;\red0\green0\blue0;\red0\green0\blue0;\red0\green0\blue0;\red0\green0\blue0;\red0\green0\blue0;\red0\green0\blue255;\red0\green0\blue0;\red0\green0\blue0;\red0\green0\blue0;\red31\green72\blue124;\red255\green0\blue255;\red0\green0\blue0;\red255\green0\blue0;\red0\green0\blue0;\red0\green0\blue0;}\viewkind1\viewscale100\margl0\margr0\margt0\margb0\deftab80\dntblnsbdb\expshrtn\paperw11900\paperh16820\pard\sb0\sl-240{\bkmkstart Pg1}{\bkmkend Pg1}\par\pard\ql \li2247\sb0\sl-322\slmult0 \par\pard\ql\li2247\sb0\sl-322\slmult0 \par\pard\ql\li2247\sb0\sl-322\slmult0 \par\pard\ql\li2247\sb0\sl-322\slmult0 \par\pard\ql\li2247\sb266\sl-322\slmult0 \up0 \expndtw-5\charscalex100 \ul0\nosupersub\cf3\f4\fs28 Algoritma Bellman-Ford dalam Distance Vector Routing Protocol \par\pard\ql \li4557\sb0\sl-253\slmult0 \par\pard\ql\li4557\sb82\sl-253\slmult0 \up0 \expndtw-4\charscalex100 \ul0\nosupersub\cf5\f6\fs24 Galih Andana\ul0\nosupersub\cf6\f7\fs20 - NIM : 13507069 \par\pard\ql \li3519\sb0\sl-230\slmult0 \par\pard\ql\li3519\sb56\sl-230\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Program Studi Teknik Informatika, Institut Teknologi Bandung \par\pard\ql \li4950\sb1\sl-217\slmult0 \up0 \expndtw-3\charscalex100 Jalan Ganesha 10, Bandung \par\pard\ql \li4542\sb13\sl-230\slmult0 \up0 \expndtw-3\charscalex100 E-mail : {\field{\*\fldinst {HYPERLINK mailto:if17069@students.if.itb.ac.id }}{\fldrslt {\ul0\nosupersub\cf7\f8\fs20 if17069@students.if.itb.ac.id}}}\par\pard\sect\sectd\sbknone\cols2\colno1\colw6130\colsr160\colno2\colw5470\colsr160\ql \li907\sb0\sl-276\slmult0 \par\pard\ql \li907\sb191\sl-276\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf5\f6\fs24 ABSTRAK\par\pard\qj \li907\sb0\sl-229\slmult0 \par\pard\qj \li907\ri464\sb5\sl-229\slmult0 \up0 \expndtw-1\charscalex100 \ul0\nosupersub\cf6\f7\fs20 Sebuah routing vektor jarak-protokol adalah salah \up0 \expndtw0\charscalex100 satu dari dua kelas utama dari routing protokol yang \up0 \expndtw0\charscalex103 digunakan dalam paket-switched network untuk \up0 \expndtw0\charscalex104 komunikasi komputer, dan kelas lainnya adalah \up0 \expndtw-2\charscalex100 protokol link-state. Algoritma Bellman-Ford di sini \up0 \expndtw-3\charscalex100 dipakai untuk menghitung path terpendek.\par\

pard\qj \li907\ri464\sb1\sl-230\slmult0\tx2749\tx3944\tx5095 \up0 \expndtw-1\charscalex100 Sebuah vektor jarak memerlukan routing protokol \line \up0 \expndtw0\charscalex103 yang menginformasikan router tetangganya dari \line \up0 \expndtw0\charscalex102 perubahan topologi secara berkala atau bila ada \line \up0 \expndtw0\charscalex102 perubahan yang terdeteksi dalam topologi jaringan. \line \up0 \expndtw0\charscalex102 Dibandingkan dengan protokol link-state, yang \line \up0 \expndtw-3\charscalex100 membutuhkan \tab \up0 \expndtw-4\charscalex100 sebuah \tab \up0 \expndtw-2\charscalex100 router \tab \up0 \expndtw-4\charscalex100 untuk\par\pard\qj \li907\ri458\sb0\sl-230\slmult0 \up0 \expndtw0\charscalex103 menginformasikan semua simpul dalam tiap \up0 \expndtw-2\charscalex100 perubahan topologi jaringan, routing vektor jarak-\line \up0 \expndtw-3\charscalex100 protokol ini memiliki komputasi yang lebih mudah.\par\pard\qj \li907\ri465\sb0\sl-230\slmult0 \up0 \expndtw-1\charscalex100 Pada makalah ini, penulis akan membahas lebih jauh \line \up0 \expndtw0\charscalex101 mengenai apa itu Bellman-Ford dan memberikan \line \up0 \expndtw0\charscalex102 sedikit perbandingan dengan algoritma routing \line \up0 \expndtw0\charscalex102 Djikstra. Di sini juga akan diberi contoh seperti apa \line \up0 \expndtw0\charscalex100 penerapan Bellman-Ford dengan studi kasus yang \line \up0 \expndtw0\charscalex105 telah penulis praktekan menggunakan bahasa \line \up0 \expndtw-3\charscalex100 pemrograman java.\par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb223\sl-230\slmult0 \up0 \expndtw-3\charscalex100 Kata kunci:\ul0\nosupersub\cf8\f9\fs20 \ul0\nosupersub\cf1\f2\fs20 Routing, Bellman-Ford, Djikstra, tetangga.\par\pard\ql \li907\sb0\sl-276\slmult0 \par\pard\ql \li907\sb186\sl-276\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf5\f6\fs24 1. PENDAHULUAN\par\pard\qj \li907\ri458\sb228\sl-229\slmult0\fi182 \up0 \expndtw0\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Para algoritma Bellman-Ford, kita menghitung satu \line \up0 \expndtw0\charscalex102 sumber jalan terpendek dalam sebuah graf berbobot \line \up0 \expndtw0\charscalex101 (bahkan di sini beberapa sisi dimungkin memiliki bobot \line \up0 \expndtw-2\charscalex100 negatif). Algoritma Dijkstra menyelesaikan masalah yang \line \up0 \expndtw0\charscalex101 sama dengan berjalan waktu yang lebih rendah, tetapi \line \up0 \expndtw0\charscalex103 memerlukan batasan di mana bobot pathnya harus non-\line \up0 \expndtw-1\charscalex100 negatif. Jadi, Bellman-Ford biasanya digunakan hanya \line \up0 \expndtw0\charscalex100 bila ada sisi negatif. Algoritma ini diberi nama Bellman-\line \up0 \expndtw-2\charscalex100 Ford karena dikembangkan oleh Richard Bellman dan \line \up0 \expndtw-3\charscalex100 Lester Ford, Jr.\par\pard\qj \li907\ri458\sb2\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex102 Menurut Robert Sedgewick, "Bobot negatif bukan \line \up0 \expndtw0\charscalex100 hanya hasil keingintahuan matematis; mereka muncul \line \up0 \expndtw0\charscalex100 secara alami ketika kita mempertimbangkan masalah-\line \up0 \expndtw0\charscalex106 masalah lain untuk menentukan jalan mana yang\par\pard\column \ql \li6290\sb0\sl-230\slmult0 \par\pard\ql \li6290\sb0\sl-230\slmult0 \par\pard\ql \li20\sb2\sl-230\slmult0 \up0 \expndtw0\charscalex101 terpendek", beliau memberikan contoh spesifik suatu\par\pard\qj \li20\ri700\sb0\sl-230\slmult0 \up0 \expndtw0\charscalex100 pengurangan dari masalah NP-lengkap graf Hamilton \up0 \expndtw0\charscalex100 untuk mencari jalan terpendek dengan beban umum. Jika \up0 \expndtw-3\charscalex100 sebuah graf berisi siklus dari total bobot jarak yang negatif \up0 \expndtw-3\charscalex100 kemudian dianggap sebagai beban terendah sehingga tidak \up0 \expndtw-3\charscalex100 ada solusi; Bellman-Ford mendeteksi kasus ini.\par\pard\qj \li20\ri700\sb0\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex104 Jika grafik berisi siklus bobot negatif, Bellman-Ford \up0 \expndtw0\charscalex103 dapat mengatasi hal ini; Tapi Bellman-Ford tidak dapat \up0 \expndtw0\charscalex100 menemukan jalan terpendek yang tidak melalui sisi yang \up0 \expndtw0\charscalex106 sama pada setiap sisi dalam suatu grafik. Masalah ini \up0 \expndtw-3\charscalex100 disebut masalah NP-lengkap jalan terpanjang.\par\pard\qj \li20\ri700\sb0\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex101 Metode ini digunakan untuk menghitung jalan terbaik \line \up0 \expndtw-1\charscalex100 untuk jaringan yang berbeda antara routing protokol yang \line \up0 \expndtw-1\charscalex100 berbeda namun fitur dasar dari algoritma ini sama dengan \line \up0 \expndtw0\charscalex104 algoritma lain

yang berbasis \ul0\nosupersub\cf8\f9\fs20 Distance Vector\ul0\nosupersub\cf1\f2\fs20 di semua \line \up0 \expndtw-3\charscalex100 protokol.\par\pard\qj \li20\ri701\sb0\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex103 Distance Vector berarti bahwa Router diposisikan \up0 \expndtw0\charscalex103 sebagai vektor yang memiliki jarak dan arah. Arah \up0 \expndtw0\charscalex100 hanyalah alamat hop berikutnya dan keluar interface dan \up0 \expndtw-3\charscalex100 Jarak berarti bobot menuju hop tersebut.\par\pard\qj \li20\ri700\sb0\sl-229\slmult0\fi182 \up0 \expndtw0\charscalex100 Router yang menggunakan protokol vektor jarak tidak \up0 \expndtw0\charscalex101 memiliki cukup pengetahuan \ul0\nosupersub\cf6\f7\fs20 seluruh jalur dari \ul0\nosupersub\cf9\f10\fs20 source \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf6\f7\fs20 ke \ul0\nosupersub\cf9\f10\fs20 destination\ul0\nosupersub\cf6\f7\fs20 , \ul0\nosupersub\cf1\f2\fs20 bahkan pada awalnya ia hanya mengetahui \up0 \expndtw-1\charscalex100 jarak antara dia dan tetangganya. Oleh sebab itu DV \up0 \expndtw-3\charscalex100 memiliki dua keterangan.\par\pard\qj \li20\ri702\sb228\sl-230\slmult0\tx313 \up0 \expndtw0\charscalex103 1.\ul0\nosupersub\cf10\f11\fs20 \ul0\nosupersub\cf1\f2\fs20 Ke mana arah atau \ul0\nosupersub\cf8\f9\fs20 interface\ul0\nosupersub\cf1\f2\fs20 yang harus dilalui oleh \line\tab \up0 \expndtw-3\charscalex100 paket untuk dapat diteruskan.\par\pard\ql \li20\sb0\sl-230\slmult0 \up0 \expndtw-2\charscalex100 2.\ul0\nosupersub\cf10\f11\fs20 \ul0\nosupersub\cf1\f2\fs20 Bobot jarak dari tujuan tersebut.\par\pard\qj \li6472\sb0\sl-229\slmult0 \par\pard\qj \li20\ri702\sb3\sl-229\slmult0\fi182 \up0 \expndtw-2\charscalex100 Seperti namanya DV protokol ini menitik beratkan pada \line \up0 \expndtw-2\charscalex100 perhitungan arah dan jarak untuk setiap link dalam sebuah \line \up0 \expndtw0\charscalex105 jaringan. Biaya untuk mencapai tujuan dihitung \line \up0 \expndtw-2\charscalex100 menggunakan berbagai rute metrik. RIP menggunakan \line \up0 \expndtw0\charscalex106 hop tujuan sedangkan IGRP mempertimbangkan \line \up0 \expndtw0\charscalex102 informasi lain seperti delay simpul dan bandwidth yang \line \up0 \expndtw-3\charscalex100 tersedia.\par\pard\qj \li20\ri695\sb3\sl-229\slmult0\fi182 \up0 \expndtw-2\charscalex100 Update dilakukan secara periodik pada protokol vektor-\line \up0 \expndtw0\charscalex100 jarak di mana semua atau bagian dari tabel routing milik \line \up0 \expndtw-3\charscalex100 router dikirim ke semua tetangga yang dikonfigurasi untuk \line \up0 \expndtw-2\charscalex100 menggunakan bobot tersebut dari protokol routing vektor-\line \up0 \expndtw0\charscalex101 jarak yang sama. RIP mendukung cross-platform, \line \up0 \expndtw-2\charscalex100 sedangkan routing vektor jarak IGRP adalah sebuah Cisco \line \up0 \expndtw-1\charscalex100 Systems protokol routing vektor jarak proprietary. Sekali \line \up0 \expndtw0\charscalex102 sebuah router yang memiliki informasi ini dapat \line \up0 \expndtw0\charscalex107 mengubah tabel routing miliknya sendiri untuk \par\pard\sect\sectd\sbknone \ql \li1123\sb0\sl-230\slmult0 \par\pard\ql\li1123\sb0\sl-230\slmult0 \par\pard\ql\li1123\sb0\sl-230\slmult0 \par\pard\ql\li1123\sb0\sl-230\slmult0 \par\pard\ql\li1123\sb228\sl-230\slmult0 \up0 \expndtw-3\charscalex100 MAKALAH IF3051 STRATEGI ALGORITMIK TAHUN 2009-2010

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0051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451401ffd9}}}}}\pard\sb0\sl-240{\bkmkstart Pg2}{\bkmkend Pg2}\par\pard\sect\sectd\sbknone\cols2\colno1\colw6130\colsr160\colno2\colw5470\colsr160\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb155\sl-230\slmult0 \up0 \expndtw-2\charscalex100 \ul0\nosupersub\cf1\f2\fs20 mencerminkan perubahan, ia kemudian memberitahu para\par\pard\qj \li907\ri465\sb2\sl-229\slmult0 \up0 \expndtw-3\charscalex100 tetangganya mengenai perubahan tersebut. Proses ini telah \up0 \expndtw-1\charscalex100 digambarkan sebagai '\ul0\nosupersub\cf8\f9\fs20 routing by rumor\ul0\nosupersub\cf1\f2\fs20 ' karena router \up0 \expndtw0\charscalex101 hanya mengandalkan informasi yang mereka terima dari \up0 \expndtw0\charscalex102 router lain dan tidak bisa menentukan apakah informasi \up0 \expndtw-3\charscalex100 tersebut benar-benar sah atau tidak.\par\pard\qj \li907\ri463\sb2\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex100 Algoritma Bellman-Ford tidak mencegah terjadinya \line \up0 \expndtw0\charscalex100 \ul0\nosupersub\cf8\f9\fs20 routing loop\ul0\nosupersub\cf1\f2\fs20 dan konsekuensi dari perhitungan untuk \line \up0 \expndtw0\charscalex104 bobot tak terhingga. Inti dari hitungan untuk bobot tak \line \up0 \expndtw0\charscalex102 terhingga adalah bahwa jika A mengatakan B yang \line \up0 \expndtw0\charscalex105 memiliki jalan di suatu tempat, tidak ada cara untuk B \line \up0 \expndtw-3\charscalex100 untuk tahu apakah jalan memiliki B sebagai sebuah bagian \line \up0 \expndtw0\charscalex100 dari itu. Untuk melihat masalah dengan jelas, bayangkan \line \up0 \expndtw0\charscalex106 sebuah subnet terhubung seperti ABCDEF, dan \line \up0 \expndtw0\charscalex103 membiarkan metrik antara router menjadi "jumlah \line \up0 \expndtw-2\charscalex100 lompatan". Sekarang anggaplah bahwa A akan turun (dari \line \up0 \expndtw0\charscalex101 order). Dalam vektor-update-proses B pemberitahuan \line \up0 \expndtw0\charscalex102 bahwa rute terpendek dari 1 sampai A sedang \ul0\nosupersub\cf8\f9\fs20 down\ul0\nosupersub\cf1\f2\fs20 - B \line \up0 \expndtw-2\charscalex100 tidak menerima update dari vektor A. Masalahnya adalah, \line \up0 \expndtw-1\charscalex100 B masih mendapatkan sebuah update dari C, dan C masih \line \up0 \expndtw0\charscalex100 belum sadar fakta bahwa A kini sedang \ul0\nosupersub\cf8\f9\fs20 down\ul0\nosupersub\cf1\f2\fs20 - sehingga \line \up0 \expndtw0\charscalex102 memberitahu B bahwa untuk pergi ke A, C hanya perlu \line \up0 \expndtw0\charscalex103 melompat dua kali. Hal ini perlahan-lahan menjalar \line \up0 \expndtw0\charscalex100 melalui jaringan sampai mencapai infinity (dalam hal ini \line \up0 \expndtw0\charscalex103 mengoreksi algoritma itu sendiri, karena adanya "\ul0\nosupersub\cf8\f9\fs20 Rilex \line \up0 \expndtw-3\charscalex100 property\ul0\nosupersub\cf1\f2\fs20 " dari Bellman Ford).\par\pard\qj \li907\ri463\sb1\sl-230\slmult0\fi182 \up0 \expndtw-3\charscalex100 Bellman-Ford memiliki struktur dasar yang sangat mirip \line \up0 \expndtw0\charscalex100 dengan Algoritma Dijkstra, tapi ia tidak dengan rakus \line \up0 \expndtw0\charscalex102 memilih simpul dengan berat minimum yang belum \line \up0 \expndtw0\charsca

lex104 diproses, dan melakukan ini | V | - 1 kali, di mana | V | \line \up0 \expndtw0\charscalex103 adalah jumlah simpul pada grafik. Repetisi tersebut \line \up0 \expndtw-3\charscalex100 memungkinkan jarak terpendek secara akurat menyebar ke \line \up0 \expndtw-2\charscalex100 seluruh grafik, karena, dengan tidak adanya siklus negatif, \line \up0 \expndtw0\charscalex102 jalan terpendek hanya dapat mengunjungi setiap simpul \line \up0 \expndtw0\charscalex103 paling banyak satu kali. Berbeda dengan Algoritma \line \up0 \expndtw-1\charscalex100 Greedy pada umumnya, yang tergantung pada asumsi \line \up0 \expndtw0\charscalex101 struktural tertentu berasal dari bobot positif, pendekatan \line \up0 \expndtw-3\charscalex100 langsung ini meluas ke kasus umum.\par\pard\qj \li907\ri463\sb4\sl-227\slmult0\fi182 \up0 \expndtw-3\charscalex100 Bellman-Ford berjalan dalam \ul0\nosupersub\cf11\f12\fs20 O\ul0\nosupersub\cf1\f2\fs20 (|V| · |E|) waktu, dimana \up0 \expndtw0\charscalex100 |V| dan |E| adalah jumlah simpul dan sisi masing-masing. \up0 \expndtw-3\charscalex100 Ide penyelesaiannya adalah :\par\pard\qj \li1190\sb0\sl-230\slmult0 \par\pard\qj \li1190\ri471\sb17\sl-230\slmult0 \up0 \expndtw0\charscalex104 Inisialisasi tabel shortest path dari source ke semua \up0 \expndtw-3\charscalex100 verteks lain kecuali dari source \u8734? ke source 0.\par\pard\qj \li1190\ri463\sb15\sl-230\slmult0 \up0 \expndtw0\charscalex102 Relaksasi tabel shortest path dalam n-1 iterasi setiap \up0 \expndtw-3\charscalex100 pasangan verteks u dan v jika sisi (u,v) ada.\par\pard\qj \li907\sb0\sl-230\slmult0 \par\pard\qj \li907\ri463\sb1\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex101 Namun dengan syarat : tidak ada siklus negatif karena \up0 \expndtw-3\charscalex100 tidak ada solusi.\par\pard\column \ql \li6290\sb0\sl-276\slmult0 \par\pard\ql \li6290\sb0\sl-276\slmult0 \par\pard\ql \li6290\sb0\sl-276\slmult0 \par\pard\ql \li6290\sb0\sl-276\slmult0 \par\pard\ql \li6290\sb0\sl-276\slmult0 \par\pard\ql \li20\sb161\sl-276\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf5\f6\fs24 2. METODE\par\pard\qj \li20\ri703\sb222\sl-230\slmult0\fi182\tx1008 \up0 \expndtw0\charscalex101 \ul0\nosupersub\cf1\f2\fs20 Algoritma Bellman-Ford dipergunakan untuk mencari \up0 \expndtw0\charscalex100 jarak terpendek pada router apabila ada sisi yang negatif \up0 \expndtw0\charscalex104 sehingga tidak dapat diselesaikan dengan algoritma \line \up0 \expndtw-3\charscalex100 Djikstra. \tab \up0 \expndtw0\charscalex107 Namun algoritma ini tidak mampu\par\pard\qj \li20\ri706\sb1\sl-230\slmult0 \up0 \expndtw0\charscalex102 menyelesaikan masalah apabila ada siklus yang bernilai \up0 \expndtw-3\charscalex100 negatif.\par\pard\qj \li20\ri702\sb0\sl-230\slmult0\fi182 \up0 \expndtw-1\charscalex100 Bobot negatif pada sebuah \ul0\nosupersub\cf8\f9\fs20 path\ul0\nosupersub\cf1\f2\fs20 mungkin saja akan \up0 \expndtw-2\charscalex100 muncul dalam masalah modeling (misalnya, seorang sopir \up0 \expndtw0\charscalex103 harus membayar uang masuk ketika melalui jalan yang \up0 \expndtw-3\charscalex100 lebih singkat, tetapi tidak untuk jalan yang lain).\par\pard\ql \li20\sb231\sl-276\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf5\f6\fs24 2.1 Penjelasan Langkah Algoritma\par\pard\ql \li6472\sb0\sl-230\slmult0 \par\pard\ql \li202\sb41\sl-230\slmult0 \up0 \expndtw0\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Anggap \u1043? = (\ul0\nosupersub\cf8\f9\fs20 V,A\ul0\nosupersub\cf1\f2\fs20 ) adalah graf berarah dan\par\pard\qj \li20\ri700\sb0\sl-235\slmult0\tx4544 \up0 \expndtw0\charscalex105 adalah fungsi jarak pada sisi \u1043?. Ibaratkan kita mencari \line \up0 \expndtw-1\charscalex100 jarak terpendek, w.r.t.\u8467?, \ul0\nosupersub\cf8\f9\fs20 path \ul0\nosupersub\cf1\f2\fs20 langsung dari \tab \up0 \expndtw-4\charscalex100 ke\par\pard\ql \li20\sb1\sl-230\slmult0\tx3396 \up0 \expndtw-1\charscalex100 semua verteks \u1043?. Kita definisikan\tab \up0 \expndtw-2\charscalex100 menjadi panjang\par\pard\ql \li20\sb6\sl-230\slmult0 \up0 \expndtw-3\charscalex100 minimal dari seluruh \ul0\nosupersub\cf8\f9\fs20 k-\ul0\nosupersub\cf1\f2\fs20 sisi dari ke\par\pard\ql \li202\sb5\sl-230\slmult0\tx2004 \up0 \expndtw-3\charscalex100 Tentunya,\tab \up0 \expndtw-2\charscalex100 (karena graf tidak boleh memiliki\par\pard\ql \li20\sb5\sl-230\slmult0\tx2460 \up0 \expndtw-3\charscalex100 siklus negatif dan\tab \up0 \expndtw-3\charscalex100 untuk semua\par\pard\ql \li202\sb0\sl-230\slmult0 \up0 \expndtw0\charscalex102 Kemudian dengan menggunakan induksi,\par\pard\ql \li2872\sb6\sl-230\slmult0 \up0 \expndtw0\charscalex109 . Hal ini baik, tapi\par\pard\qj \li20\ri701\sb0\sl-231\slmult0\tx3338 \up0 \expndtw0\charscalex101 apakah \ul0\nosupersub\cf8\f

9\fs20 k\ul0\nosupersub\cf1\f2\fs20 dapat tumbuh tiba-tiba? Jika kita mengunjungi \line \up0 \expndtw-1\charscalex100 verteks lebih dari sekali, ini berarti graf mengandung \line \up0 \expndtw0\charscalex100 siklik, kecuali bila siklik tersebut mengandung bobot \line \up0 \expndtw0\charscalex104 negatif, kita dapat menghilangkannya, dan tidak \line \up0 \expndtw0\charscalex102 menambah panjang jalan. Jadi, tanpa kehilangan secara \line \up0 \expndtw0\charscalex102 general, sebuah jalan terpendek ke \tab \up0 \expndtw0\charscalex100 memiliki hampir\par\pard\ql \li20\sb5\sl-230\slmult0\tx2930 \up0 \expndtw-1\charscalex100 semua verteks |V|, dan juga\tab \up0 \expndtw0\charscalex101 adalah jarak dari ke\par\pard\qj \li20\ri702\sb227\sl-235\slmult0\fi182 \up0 \expndtw-1\charscalex100 Maka pada hampir semua \ul0\nosupersub\cf11\f12\fs20 O\ul0\nosupersub\cf1\f2\fs20 (|V| · |E|) operasi, kita akan \up0 \expndtw-3\charscalex100 menemukan jarak dari ke setiap verteks dari \u1043?.\par\pard\ql \li20\sb237\sl-276\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf5\f6\fs24 2.2 Langkah Algoritma\par\pard\qj \li20\ri701\sb223\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Algoritma ini, seperti algoritma djikstra menggunakan \up0 \expndtw0\charscalex104 tepi relaksasi tetapi tidak memakai metode greedy. \up0 \expndtw0\charscalex104 Bahkan, ini menggunakan d[u] sebagai batas atas pada \up0 \expndtw-3\charscalex100 jarak d[u,v] dari u ke v.\par\pard\qj \li20\ri700\sb2\sl-229\slmult0\fi182 \up0 \expndtw-2\charscalex100 Algortima ini secara berkala mengurangi perkiraan d[v] \line \up0 \expndtw0\charscalex100 pada bobot dari jalan terpendek dari sumber verteks s ke \line \up0 \expndtw-2\charscalex100 tiap verteks v pada V hingga memperoleh jalan terpendek. \line \up0 \expndtw0\charscalex104 Berikut ini penulis melampirkan langkah-langkah \line \up0 \expndtw-2\charscalex100 penyusunan algoritmanya yang akan mengembalikan nilai \line \up0 \expndtw0\charscalex104 TRUE jika pada graf tidak terdapat siklus yang negatif \line \up0 \expndtw-3\charscalex100 dan akan mengembalikan nilai FALSE jika sebaliknya. \par\pard\sect\sectd\sbknone \ql \li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb206\sl-230\slmult0 \up0 \expndtw-3\charscalex100 MAKALAH IF3051 STRATEGI ALGORITMIK TAHUN 2009-2010 \par\pard\sect\sectd\fs24\paperw11900\paperh16820{\shp{\*\shpinst\shpleft0\shptop0\shpright11900\shpbottom16820\shpwr3\shpfblwtxt0\shpz-10000\shplid2{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn pib}{\sv {\pict\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0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a0028a28a00ffd9}}}}}\pard\sb0\sl-240{\bkmkstart Pg3}{\bkmkend Pg3}\par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb170\sl-230\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf12\f13\fs20 BELLMAN-FORD\ul0\nosupersub\cf6\f7\fs20 (G, \ul0\nosupersub\cf9\f10\fs20 w\ul0\nosupersub\cf6\f7\fs20 , \ul0\nosupersub\cf9\f10\fs20 s\ul0\nosupersub\cf6\f7\fs20 )\par\pard\sect\sectd\sbknone\cols2\colno1\colw6130\colsr160\colno2\colw5470\colsr160\ql \li907\sb19\sl-225\slmult0\tx1329 \up0 \expndtw-4\charscalex100 \ul0\nosupersub\cf1\f2\fs20 1.\tab \up0 \expndtw-3\charscalex100 INITIALIZE-SINGLE-SOURCE (G, \ul0\nosupersub\cf8\f9\fs20 s\ul0\nosupersub\cf1\f2\fs20 )\par\pard\ql \li907\sb1\sl-230\slmult0\tx1329 \up0 \expndtw-4\charscalex100 2.\tab \up0 \expndtw-3\charscalex100 for each vertex \ul0\nosupersub\cf8\f9\fs

20 i\ul0\nosupersub\cf1\f2\fs20 = 1 to V[G] - 1 do\par\pard\ql \li907\sb1\sl-230\slmult0\tx1536 \up0 \expndtw-4\charscalex100 3.\tab \up0 \expndtw-3\charscalex100 for each edge (u, \ul0\nosupersub\cf8\f9\fs20 v\ul0\nosupersub\cf1\f2\fs20 ) in E[G] do\par\pard\ql \li907\sb1\sl-230\slmult0\tx1733 \up0 \expndtw-4\charscalex100 4.\tab \up0 \expndtw-4\charscalex100 RELAX (u, \ul0\nosupersub\cf8\f9\fs20 v\ul0\nosupersub\cf1\f2\fs20 , \ul0\nosupersub\cf8\f9\fs20 w\ul0\nosupersub\cf1\f2\fs20 )\par\pard\ql \li907\sb0\sl-225\slmult0\tx1329 \up0 \expndtw-4\charscalex100 5.\tab \up0 \expndtw-3\charscalex100 For each edge (u, \ul0\nosupersub\cf8\f9\fs20 v\ul0\nosupersub\cf1\f2\fs20 ) in E[G] do\par\pard\ql \li907\sb2\sl-230\slmult0\tx1531 \up0 \expndtw-4\charscalex100 6.\tab \up0 \expndtw-3\charscalex100 if d[u] + \ul0\nosupersub\cf8\f9\fs20 w\ul0\nosupersub\cf1\f2\fs20 (u, \ul0\nosupersub\cf8\f9\fs20 v\ul0\nosupersub\cf1\f2\fs20 ) < d[\ul0\nosupersub\cf8\f9\fs20 v]\ul0\nosupersub\cf1\f2\fs20 then\par\pard\ql \li907\sb0\sl-230\slmult0\tx1728 \up0 \expndtw-4\charscalex100 7.\tab \up0 \expndtw-3\charscalex100 return FALSE\par\pard\ql \li907\sb0\sl-230\slmult0\tx1329 \up0 \expndtw-4\charscalex100 8.\tab \up0 \expndtw-4\charscalex100 return TRUE\par\pard\qj \li907\ri458\sb1\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex103 Inisialisasi pada line 1 memerlukan waktu O(v) time. \up0 \expndtw0\charscalex104 Untuk loop dari line 2-4 memerlukan waktu O(E) dan \up0 \expndtw-3\charscalex100 untuk line 5-7 memerlukan O(E) time pula. Jadi, Bellman-\line \up0 \expndtw-3\charscalex100 Ford berjalan dalam kompleksitas waktu O(E) time.\par\pard\ql \li907\sb236\sl-276\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf5\f6\fs24 2.3 Pseudocode Algoritma Bellman-Ford\par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb0\sl-207\slmult0 \par\pard\ql \li1618\sb44\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Gambar 1. Pseudocode menurut wikipedia\par\pard\ql \li907\sb0\sl-276\slmult0 \par\pard\ql \li907\sb132\sl-276\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf5\f6\fs24 2.4 Contoh Routing dengan Bellman-Ford\par\pard\ql \li1090\sb223\sl-230\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Dalam jaringan ini kita punya 4 router A, B, C, D:\par\pard\ql \li1421\sb0\sl-207\slmult0 \par\pard\ql \li1421\sb0\sl-207\slmult0 \par\pard\ql \li1421\sb0\sl-207\slmult0 \par\pard\ql \li1421\sb0\sl-207\slmult0 \par\pard\ql \li1421\sb0\sl-207\slmult0 \par\pard\ql \li1421\sb0\sl-207\slmult0 \par\pard\ql \li1421\sb0\sl-207\slmult0 \par\pard\ql \li1421\sb0\sl-207\slmult0 \par\pard\ql \li1421\sb24\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Gambar 2. Router A, B, C, D dan Bobot Sisinya\par\pard\qj \li907\ri463\sb222\sl-229\slmult0\fi182 \up0 \expndtw0\charscalex103 \ul0\nosupersub\cf1\f2\fs20 Penulis menandai waktu saat ini (atau iterasi) dalam \line \up0 \expndtw-2\charscalex100 algoritma dengan T, dan akan mulai (pada waktu 0, atau T \line \up0 \expndtw-2\charscalex100 = 0) dengan membuat matriks jarak untuk setiap router ke \line \up0 \expndtw0\charscalex103 tetangga terdekatnya. tabel routing di bawah ini, jalan \line \up0 \expndtw0\charscalex103 terpendek akan disorot dengan warna hijau, dan update \line \up0 \expndtw-3\charscalex100 untuk jalan terpendek baru disorot dengan warna kuning.\par\pard\column \ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li1153\sb78\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Tabel 1 Routing Table saat T=0\par\pard\ql \li202\sb221\sl-230\slmult0 \up0 \expndtw0\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Pada titik ini, semua router \up0 \expndtw-1\charscalex100 (A, B, C, D) memiliki\par\pard\qj \li20\ri701\sb1\sl-229\slmult0 \up0 \expndtw0\charscalex101 "jalan-terpendek" untuk DV mereka (

daftar jarak yang \up0 \expndtw0\charscalex100 berasal dari mereka ke router lain melalui tetangga). \up0 \expndtw-2\charscalex100 Mereka masing-masing mengirimkan DV baru ini kepada \up0 \expndtw0\charscalex101 semua tetangga mereka: A ke B dan C, B ke C dan A, C \up0 \expndtw0\charscalex107 ke A, B, dan D, dan D ke C. tetangga masing-masing \up0 \expndtw-3\charscalex100 menerima informasi ini, kemudian menghitung ulang yang \up0 \expndtw-3\charscalex100 jalur terpendek digunakannya.\par\pard\qj \li20\ri695\sb2\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex102 Sebagai contoh: A menerima sebuah DV dari C yang \line \up0 \expndtw0\charscalex106 menyatakan A ada jalur melalui C ke D, dengan jarak \line \up0 \expndtw0\charscalex105 (atau biaya) 5. Karena saat ini "jalan terpendek" ke C \line \up0 \expndtw-1\charscalex100 adalah 23, maka A tahu itu jalan ke D bahwa biaya 23 +5 \line \up0 \expndtw0\charscalex100 = 28. Karena tidak ada jalan lain yang lebih pendek yang \line \up0 \expndtw0\charscalex100 diketahui A, ia menempatkan ini sebagai perkiraan arus-\line \up0 \expndtw-3\charscalex100 jalan terpendek dari dirinya sendiri (A) ke D, via C.\par\pard\ql \li7423\sb0\sl-207\slmult0 \par\pard\ql \li7423\sb0\sl-207\slmult0 \par\pard\ql \li7423\sb0\sl-207\slmult0 \par\pard\ql \li7423\sb0\sl-207\slmult0 \par\pard\ql \li7423\sb0\sl-207\slmult0 \par\pard\ql \li7423\sb0\sl-207\slmult0 \par\pard\ql \li7423\sb0\sl-207\slmult0 \par\pard\ql \li1153\sb140\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Tabel 2 Routing Table saat T=1\par\pard\qj \li20\ri702\sb221\sl-229\slmult0\fi182 \up0 \expndtw0\charscalex101 \ul0\nosupersub\cf1\f2\fs20 Sekali lagi, semua router telah diperoleh dalam iterasi \up0 \expndtw0\charscalex100 terakhir (pada T = 1) "jalan terpendek", sehingga mereka \up0 \expndtw-2\charscalex100 semua menyiarkan DV mereka pada tetangga mereka; Hal \up0 \expndtw-2\charscalex100 ini mendorong masing-masing tetangga untuk kembali \up0 \expndtw-3\charscalex100 menghitung jarak terpendek mereka lagi.\par\pard\qj \li20\ri700\sb1\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex102 Sebagai contoh: A menerima sebuah DV dari B yang \up0 \expndtw0\charscalex103 memberitahu A ada jalur melalui B ke D, dengan jarak \up0 \expndtw-1\charscalex100 (atau biaya) dari \up0 \expndtw-1\charscalex100 7. Karena saat ini "jalan-terpendek"\par\pard\qj \li20\ri701\sb0\sl-230\slmult0 \up0 \expndtw0\charscalex105 untuk B adalah 3, maka A mengetahui ada jalan ke D \line \up0 \expndtw-2\charscalex100 dengan biaya 7 +3 = 10. Jalan ke D ini dengan panjang 10 \line \up0 \expndtw-2\charscalex100 (melalui B) lebih pendek daripada "jalan-terpendek" ke D \line \up0 \expndtw-2\charscalex100 dengan panjang \up0 \expndtw-1\charscalex100 28 (melalui C), sehingga \up0 \expndtw-2\charscalex100 10 tersebut\par\pard\ql \li20\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 menjadi "jalan-terpendek" ke D yang baru.\par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li1153\sb6\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Tabel 3 Routing Table saat T=2\par\pard\qj \li20\ri700\sb221\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex107 \ul0\nosupersub\cf1\f2\fs20 Kali ini, hanya router A dan D yang memiliki jalan \line \up0 \expndtw0\charscalex102 terpendek baru untuk dvs. Jadi, mereka menyiarkan DV \line \up0 \expndtw0\charscalex101 baru mereka kepada tetangga mereka: A mengirim ke B \par\pard\sect\sectd\sbknone \ql \li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb96\sl-230\slmult0 \up0 \expndtw-3\charscalex100 MAKALAH IF3051 STRATEGI ALGORITMIK TAHUN 2009-2010 \par\pard\sect\sectd\fs24\paperw11900\paperh16820{\shp{\*\shpinst\shpleft0\shptop0\shpright11900\shpbottom16820\shpwr3\shpfblwtxt0\shpz-10000\shplid3{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fBehindDocument}{\sv 1}}{\sp{\sn pib}{\sv {\pict\jpegblipffd8ffe000104a46494600010101006000600000ffdb00430001010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101ffdb00430101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101ffc0

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1400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451400514514005145140051451401ffd9}}}}}\pard\sb0\sl-240{\bkmkstart Pg4}{\bkmkend Pg4}\par\pard\qj \li907\sb0\sl-232\slmult0 \par\pard\qj\li907\sb0\sl-232\slmult0 \par\pard\qj\li907\sb0\sl-232\slmult0 \par\pard\qj\li907\sb0\sl-232\slmult0 \par\pard\qj\li907\sb0\sl-232\slmult0 \par\pard\qj\li907\sb0\sl-232\slmult0 \par\pard\qj\li907\ri6124\sb157\sl-232\slmult0 \up0 \expndtw0\charscalex105 \ul0\nosupersub\cf1\f2\fs20 dan C, dan D mengirim pada C. Hal ini menyebabkan \line \up0 \expndtw-1\charscalex100 masing-masing dari tetangga menerima DV baru, dan \line \up0 \expndtw0\charscalex100 kembali menghitung jalan terpendek mereka. Namun, \line \up0 \expndtw0\charscalex105 karena informasi dari DV tidak menghasilkan apa pun \line \up0 \expndtw-1\charscalex100 jalan-jalan lebih pendek daripada yang sudah ada di tabel \line \up0 \expndtw-1\charscalex100 routing mereka, maka tidak ada perubahan pada tabel\par\pard\sect\sectd\sbknone\cols2\colno1\colw6130\colsr160\colno2\colw5470\colsr160\ql \li907\sb2\sl-230\slmult0 \up0 \expndtw-3\charscalex100 routing.\par\pard\ql \li2041\sb0\sl-207\slmult0 \par\pard\ql \li2041\sb0\sl-207\slmult0 \par\pard\ql \li2041\sb0\sl-207\slmult0 \par\pard\ql \li2041\sb0\sl-207\slmult0 \par\pard\ql \li2041\sb0\sl-207\slmult0 \par\pard\ql \li2041\sb0\sl-207\slmult0 \par\pard\ql \li2041\sb0\sl-207\slmult0 \par\pard\ql \li2041\sb6\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Tabel 4 Routing Table saat T=3\par\pard\qj \li907\ri469\sb220\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Tidak ada router lagi yang memiliki \u8220?jalan terpendek\u8221? \line \up0 \expndtw0\charscalex100 baru. Maka tidak ada router yang memperoleh informasi \line \up0 \expndtw0\charscalex101 baru yang memungkinkan terjadinya perubahan pada \line \up0 \expndtw0\charscalex100 routing table mereka. Dengan kata lain algortima ini \line \up0 \expndtw-3\charscalex100 selesai.\par\pard\ql \li907\sb236\sl-276\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf5\f6\fs24 2.5 Kelemahan Algoritma dan Solusinya\par\pard\qj \li907\ri464\sb224\sl-229\slmult0\fi182 \up0 \expndtw0\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Pada algoritma ini apabila kita menghadapi perubahan \up0 \expndtw0\charscalex103 link cost pada suatu node, kita harus melakukan update \up0 \expndtw0\charscalex101 pada DV yang ada. Bila cost yang diubah menjadi lebih \up0 \expndtw0\charscalex100 kecil, seluruh DV akan otomatis berubah karena ada \up0 \expndtw0\charscalex102 penggantian link cost yang lebih minimum. Namun, \up0 \expndtw-1\charscalex100 apabila kita mengganti link cost dengan angka yang lebih \up0 \expndtw-2\charscalex100 besar akan ada kemungkinan terjadinya \ul0\nosupersub\cf8\f9\fs20 infinite loop \ul0\nosupersub\cf1\f2\fs20 (loop \up0 \expndtw0\charscalex105 abadi). Hal tersebut juga dapat terjadi apabila ada \up0 \expndtw0\charscalex103 permasalah pemutusan link dari suatu node dengan \up0 \expndtw-3\charscalex100 mengganti bobot linknya menjadi 999.\par\pard\qj \li907\ri467\sb2\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex103 Berikut penjelasan secara rincinya dengan contoh \up0 \expndtw-3\charscalex100 berikut.\par\pard\ql \li1781\sb0\sl-207\slmult0 \par\pard\ql \li1781\sb0\sl-207\slmult0 \par\pard\ql \li1781\sb0\sl-207\slmult0 \par\pard\ql \li1781\sb0\sl-207\slmult0 \par\pard\ql \li1781\sb0\sl-207\slmult0 \par\pard\ql \li1781\sb0\sl-207\slmult0 \par\pard\ql \li1781\sb0\sl-207\slmult0 \par\pard\ql \li1781\sb50\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Gambar 3. Kasus pada Router A, B, C\par\pard\ql \li907\sb196\sl-230\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Pada mulanya routing table yang terbentuk di A adalah\par\pard\ql \li2933\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 A-B = 3\par\pard\ql \li2933\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 A-C = 5\par\pard\ql \li907\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 sedangkan di B adalah\par\pard\ql \li2933\sb0\sl-225\slmult0 \up0 \expndtw-3\charscalex100 B-A = 3\par\pard\ql \li2938\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 B-C = 2\par\pard\ql \li907\sb1\sl

-230\slmult0 \up0 \expndtw-3\charscalex100 dan di C adalah\par\pard\ql \li2962\sb1\sl-230\slmult0 \up0 \expndtw-4\charscalex100 C-A = 5\par\pard\ql \li2938\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 C-B = 2\par\pard\column \ql \li159\sb73\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Gambar 4. Seakan-akan Ada Path pada Router A-C, C-A\par\pard\qj \li20\ri704\sb221\sl-230\slmult0\fi182 \up0 \expndtw-1\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Hal ini akan terus berlangsung selama tidak terjadi \up0 \expndtw0\charscalex102 perubahan. Bila terjadi proses update link cost antara B \up0 \expndtw-3\charscalex100 dan C menjadi 1.\par\pard\ql \li6640\sb0\sl-207\slmult0 \par\pard\ql \li6640\sb0\sl-207\slmult0 \par\pard\ql \li6640\sb0\sl-207\slmult0 \par\pard\ql \li6640\sb0\sl-207\slmult0 \par\pard\ql \li6640\sb0\sl-207\slmult0 \par\pard\ql \li6640\sb0\sl-207\slmult0 \par\pard\ql \li6640\sb0\sl-207\slmult0 \par\pard\ql \li370\sb15\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Gambar 5. Update Cost pada Router B-C menjadi 1\par\pard\qj \li20\ri702\sb221\sl-230\slmult0 \up0 \expndtw0\charscalex101 \ul0\nosupersub\cf1\f2\fs20 Maka B akan mengirimkan paket ke tetangganya (A, C) \line \up0 \expndtw0\charscalex102 bahwa ada jalan baru dari B-C dengan cost 1. Karena C \line \up0 \expndtw0\charscalex104 memiliki cost dari C-B dengan bobot minimum \up0 \expndtw-4\charscalex100 2,\par\pard\qj \li20\ri701\sb3\sl-227\slmult0 \up0 \expndtw0\charscalex101 sedangkan ada update dari B bahwa ada jalan yang \line \up0 \expndtw0\charscalex102 melalui B-C dengan bobot 1 (di mana 1 < 2), C akan \line \up0 \expndtw-2\charscalex100 mengganti cost \up0 \expndtw-2\charscalex100 \u8220?jalan-terpendek\u8221? dari C-B menjadi \up0 \expndtw-4\charscalex100 1.\par\pard\qj \li20\ri700\sb2\sl-230\slmult0 \up0 \expndtw0\charscalex100 Dan hal ini mempengaruhi Kemudian router A yang \up0 \expndtw0\charscalex101 tadinya memiliki cost link antara A-C yang sebelumnya \up0 \expndtw-3\charscalex100 bernilai \up0 \expndtw0\charscalex103 5, mendapat informasi dari B bahwa ada \ul0\nosupersub\cf8\f9\fs20 path\par\pard\qj \li20\ri700\sb0\sl-230\slmult0 \up0 \expndtw-1\charscalex100 \ul0\nosupersub\cf1\f2\fs20 baru dari B-C dengan nilai 1, ia akan mengganti cost A-C \up0 \expndtw-3\charscalex100 yang sebelumnya 5 dengan 3+1=4, karena 4 < 5. Sehingga \up0 \expndtw-3\charscalex100 kini routing table yang terbentuk di A adalah\par\pard\ql \li2047\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 A-B = 3\par\pard\ql \li2047\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 A-C = 4\par\pard\ql \li20\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 sedangkan di B adalah\par\pard\ql \li2047\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 B-A = 3\par\pard\ql \li2051\sb1\sl-225\slmult0 \up0 \expndtw-3\charscalex100 B-C = 1\par\pard\ql \li20\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 dan di C adalah\par\pard\ql \li2075\sb1\sl-230\slmult0 \up0 \expndtw-4\charscalex100 C-A = 4\par\pard\ql \li2051\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 C-B = 1\par\pard\ql \li7255\sb0\sl-207\slmult0 \par\pard\ql \li7255\sb0\sl-207\slmult0 \par\pard\ql \li7255\sb0\sl-207\slmult0 \par\pard\ql \li7255\sb0\sl-207\slmult0 \par\pard\ql \li7255\sb0\sl-207\slmult0 \par\pard\ql \li7255\sb0\sl-207\slmult0 \par\pard\ql \li7255\sb0\sl-207\slmult0 \par\pard\ql \li7255\sb0\sl-207\slmult0 \par\pard\ql \li985\sb39\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Gambar 6. Distance Cost yang Baru\par\pard\qj \li20\ri701\sb221\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Namun hal tersebut akan berdampak buruk apabila \up0 \expndtw0\charscalex100 penggantian cost tersebut melebihi \ul0\nosupersub\cf8\f9\fs20 pseudo path \ul0\nosupersub\cf1\f2\fs20 yang \up0 \expndtw0\charscalex101 terbentuk pada node A-C. Misalkan kita mematikan link \up0 \expndtw-3\charscalex100 antara B-C dan mengesetnya menjadi 999. \par\pard\sect\sectd\sbknone \ql \li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb88\sl-230\slmult0 \up0 \expndtw-3\charscalex100 MAKALAH IF3051 STRATEGI ALGORITMIK TAHUN 2009-2010 \par\pard\sect\sectd\fs24\paperw11900\paperh16820{\shp{\*\shpinst\shpleft0\shptop0\shpright11900\shpbottom16820\shpwr3\shpfblwtxt0\shpz-10000\shplid4{\sp{\sn shapeType}{\sv 75}}

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ar 7. Link Antara B-C Diset Menjadi 999\par\pard\qj \li907\ri465\sb220\sl-230\slmult0 \up0 \expndtw0\charscalex102 \ul0\nosupersub\cf1\f2\fs20 Hal pertama yang dilakukan router B adalah mengubah \up0 \expndtw-3\charscalex100 cost dari B-C menjadi 999. routing table yang terbentuk di \up0 \expndtw-3\charscalex100 A adalah tetap\par\pard\ql \li2933\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 A-B = 3\par\pard\ql \li2933\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 A-C = 4\par\pard\ql \li907\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 sedangkan di B adalah\par\pard\ql \li2933\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 B-A = 3\par\pard\ql \li2837\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 B-C = 999\par\pard\ql \li907\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 dan di C pun ikut mengganti bobot path C-B\par\pard\ql \li2962\sb0\sl-230\slmult0 \up0 \expndtw-4\charscalex100 C-A = 4\par\pard\ql \li2813\sb1\sl-225\slmult0 \up0 \expndtw-3\charscalex100 C-B = 999.\par\pard\qj \li907\ri467\sb2\sl-230\slmult0 \up0 \expndtw0\charscalex104 Tetapi ketika router B akan mengirimkan paket update \line \up0 \expndtw0\charscalex103 kepada tetangganya, router A dan C akan mengirimkan \line \up0 \expndtw-1\charscalex100 paket DV mereka terlebih dahulu di mana masih terdapat \line \up0 \expndtw0\charscalex104 \ul0\nosupersub\cf8\f9\fs20 pseudo-path \ul0\nosupersub\cf1\f2\fs20 antara A-C dengan bobot \up0 \expndtw0\charscalex112 4. B yang\par\pard\qj \li907\ri463\sb0\sl-230\slmult0 \up0 \expndtw-1\charscalex100 mengetahui hal ini akan memilih jalur B-A-C dengan \up0 \expndtw-4\charscalex100 bobot \up0 \expndtw0\charscalex105 3+4=7 karena lebih kecil dari \up0 \expndtw0\charscalex106 999. B akan\par\pard\ql \li907\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 mengganti path yang ia miliki menjadi 7.\par\pard\ql \li2933\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 B-A = 3\par\pard\ql \li2938\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 B-C = 7\par\pard\ql \li907\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 Setelah itu barulah router A berubah menjadi\par\pard\ql \li2933\sb0\sl-225\slmult0 \up0 \expndtw-3\charscalex100 A-B = 3\par\pard\ql \li2832\sb2\sl-230\slmult0 \up0 \expndtw-3\charscalex100 A-C = 999\par\pard\ql \li907\sb230\sl-230\slmult0 \up0 \expndtw-3\charscalex100 Router C kini telah terputus\par\pard\ql \li1666\sb0\sl-207\slmult0 \par\pard\ql \li1666\sb0\sl-207\slmult0 \par\pard\ql \li1666\sb0\sl-207\slmult0 \par\pard\ql \li1666\sb0\sl-207\slmult0 \par\pard\ql \li1666\sb0\sl-207\slmult0 \par\pard\ql \li1666\sb0\sl-207\slmult0 \par\pard\ql \li1666\sb0\sl-207\slmult0 \par\pard\ql \li1666\sb0\sl-207\slmult0 \par\pard\ql \li1666\sb54\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Gambar 8. Perubahan Link Hasil Update\par\pard\qj \li907\ri463\sb221\sl-230\slmult0\fi182 \up0 \expndtw-1\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Masalah tersebut belum berhenti karena sebelum B \line \up0 \expndtw-2\charscalex100 sempat mengganti link cost ke C miliknya menjadi 999, A \line \up0 \expndtw0\charscalex104 telah menerima update bahwa ada link cost antara B-C \line \up0 \expndtw-2\charscalex100 yang bernilai 7, sehingga A akan menemukan jalan bahwa \line \up0 \expndtw0\charscalex101 ternyata ada jalan ke router C yang lebih minimum \line \up0 \expndtw-1\charscalex100 melalui A-B-C sebesar \up0 \expndtw-3\charscalex100 3+7=10, \up0 \expndtw-2\charscalex100 (10 \up0 \expndtw-1\charscalex100 < 999) sehingga\par\pard\ql \li907\sb0\sl-230\slmult0 \up0 \expndtw0\charscalex106 router A akan mengganti cost \up0 \expndtw-3\charscalex100 \u8220?jalan-terpendek\u8221?nya\par\pard\ql \li907\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 menjadi\par\pard\ql \li2933\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 A-B = 3\par\pard\ql \li2881\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 A-C = 10\par\pard\ql \li907\sb0\sl-225\slmult0 \up0 \expndtw-3\charscalex100 Setelah itu barulah router B berubah menjadi\par\pard\ql \li2933\sb2\sl-230\slmult0 \up0 \expndtw-3\charscalex100 B-A = 3\par\pard\ql \li2837\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 B-C = 999\par\pard\column \ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li1028\sb87

\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Gambar 9. Perubahan Selanjutnya\par\pard\qj \li20\ri701\sb221\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex101 \ul0\nosupersub\cf1\f2\fs20 Dan hal ini kan berlangsung secara terus menerus \up0 \expndtw-1\charscalex100 hingga kedua sisi mencapai angka maksimum putus yaitu \up0 \expndtw-3\charscalex100 999. Hal inilah yang dikatakan sebagai \ul0\nosupersub\cf8\f9\fs20 infinite loop.\par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li1340\sb160\sl-207\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf13\f14\fs18 Gambar 10. Kondisi Akhir\par\pard\qj \li20\ri700\sb221\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex107 \ul0\nosupersub\cf1\f2\fs20 Untungnya, hal tersebut dapat diatasi dengan \line \up0 \expndtw-2\charscalex100 menggunakan perintah untuk melakukan Bellman-Ford \line \up0 \expndtw-1\charscalex100 ulang setiap kali ada perubahan link cost. Kita dapat \line \up0 \expndtw-2\charscalex100 menggunakan boolean UPDATE yang bernilai FALSE \line \up0 \expndtw-1\charscalex100 saat awal dan bernilai TRUE bila ada perubahan link cost \line \up0 \expndtw0\charscalex101 yang terjadi. Setiap kita melakukan update link cost kita \line \up0 \expndtw-3\charscalex100 akan mengeset boolean UPDATE menjadi TRUE. Apabila \line \up0 \expndtw0\charscalex103 boolean UPDATE bernilai TRUE, seluruh router wajib \line \up0 \expndtw0\charscalex101 melakukan \ul0\nosupersub\cf14\f15\fs20 Bellman-Ford ulang dari susunan toplogy \line \up0 \expndtw0\charscalex101 router yang baru\ul0\nosupersub\cf1\f2\fs20 , oleh sebab itu kita perlu mencatat link \line \up0 \expndtw0\charscalex103 cost antar tetangga terbaru yang ada pada setiap router. \line \up0 \expndtw-1\charscalex100 Apabila kita melakukan Bellman-Ford ulang, otomatis \line \up0 \expndtw0\charscalex101 masalah mengenai perubahan cost dari B-C di atas tidak \line \up0 \expndtw0\charscalex102 akan berpengaruh sebab sejak awal C sudah dianggap \line \up0 \expndtw-3\charscalex100 telah \ul0\nosupersub\cf8\f9\fs20 down\ul0\nosupersub\cf1\f2\fs20 dan tidak diperhitungkan dalam algoritma ini.\par\pard\ql \li6290\sb0\sl-276\slmult0 \par\pard\ql \li20\sb191\sl-276\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf5\f6\fs24 IV. KESIMPULAN\par\pard\qj \li20\ri700\sb223\sl-230\slmult0\fi182 \up0 \expndtw0\charscalex100 \ul0\nosupersub\cf1\f2\fs20 Sebuah varian dari algoritma Bellman-Ford biasanya \up0 \expndtw0\charscalex100 digunakan dalam protokol routing vektor jarak, misalnya \up0 \expndtw0\charscalex102 Routing Information Protocol \up0 \expndtw0\charscalex103 (RIP). Algoritma ini\par\pard\qj \li20\ri701\sb0\sl-230\slmult0 \up0 \expndtw-1\charscalex100 didistribusikan karena melibatkan sejumlah node (router) \up0 \expndtw-1\charscalex100 dalam sebuah sistem Otonom, dan koleksi jaringan IPnya \up0 \expndtw0\charscalex102 biasanya dimiliki oleh sebuah ISP. Algoritma ini terdiri \up0 \expndtw-3\charscalex100 dari langkah-langkah berikut:\par\pard\ql \li6290\sb0\sl-228\slmult0 \par\pard\ql \li20\ri705\sb4\sl-228\slmult0\tx313\tx313 \up0 \expndtw-1\charscalex100 1.\ul0\nosupersub\cf10\f11\fs20 \ul0\nosupersub\cf1\f2\fs20 Setiap simpul menghitung jarak antara dirinya dan \line\tab \up0 \expndtw-1\charscalex100 semua node lain dalam AS dan menyimpan informasi \line \tab \up0 \expndtw-3\charscalex100 ini dalam sebuah tabel.\par\pard\qj \li20\ri705\sb1\sl-230\slmult0\tx313 \up0 \expndtw0\charscalex100 2.\ul0\nosupersub\cf10\f11\fs20 \ul0\nosupersub\cf1\f2\fs20 Setiap node mengirimkan tabel untuk semua node \line\tab \up0 \expndtw-3\charscalex100 tetangganya.\par\pard\ql \li20\ri700\sb0\sl-230\slmult0\tx313\tx313\tx313 \up0 \expndtw0\charscalex107 3.\ul0\nosupersub\cf10\f11\fs20 \ul0\nosupersub\cf1\f2\fs20 Ketika sebuah node menerima tabel jarak dari \line\tab \up0 \expndtw-3\charscalex100 tetangga-tetangganya, ia menghitung rute terpendek ke \line \tab \up0 \expndtw-1\charscalex100 semua node lainnya dan melakukan updating tabelnya \line \tab \up0 \expndtw-3\charscalex100 sendiri untuk mencerminkan perubahan apapun. \par\pard\sect\sectd\sbknone \ql \li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb87\sl-230\slmult0 \up0 \expndtw-3\charscalex100 MAKALAH IF3051 STRATEGI ALGORITMIK TAHUN 2009-2010 \par\pard\sect\sectd\fs24\paperw11900\paperh16820\pard\sb0\sl-240{\bkmkstart Pg6}{\bkmkend Pg6}\par\pard\sect\sectd\sbknone\cols2\

colno1\colw6130\colsr160\colno2\colw5470\colsr160\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li1090\sb155\sl-230\slmult0 \up0 \expndtw0\charscalex101 \ul0\nosupersub\cf1\f2\fs20 Kelemahan utama dari algoritma Bellman-Ford dalam\par\pard\ql \li907\sb1\sl-230\slmult0 \up0 \expndtw-3\charscalex100 latar protokol routing untuk vektor jarak adalah:\par\pard\ql \li907\sb0\sl-230\slmult0 \par\pard\ql \li907\sb1\sl-230\slmult0\tx1329 \up0 \expndtw-4\charscalex100 1.\tab \up0 \expndtw-3\charscalex100 Perhitungan skala kurang baik\par\pard\ql \li907\sb1\sl-230\slmult0\tx1329 \up0 \expndtw-4\charscalex100 \ul0\nosupersub\cf8\f9\fs20 2.\tab \up0 \expndtw0\charscalex101 \ul0\nosupersub\cf1\f2\fs20 Perubahan dalam topologi jaringan tidak tercermin\par\pard\ql \li1334\sb0\sl-225\slmult0 \up0 \expndtw0\charscalex100 dengan cepat sejak pembaruan menyebar karena\par\pard\ql \li1334\sb2\sl-230\slmult0 \up0 \expndtw-3\charscalex100 dilakukan node-by-node bukan broadcasting.\par\pard\ql \li907\sb0\sl-230\slmult0\tx1329 \up0 \expndtw-4\charscalex100 3.\tab \up0 \expndtw0\charscalex100 \ul0\nosupersub\cf8\f9\fs20 Counting to infinity\ul0\nosupersub\cf1\f2\fs20 (jika link atau node mengalami\par\pard\ql \li1334\sb0\sl-230\slmult0 \up0 \expndtw0\charscalex102 kegagalan dan menjadikan sebuah simpul tidak\par\pard\ql \li1334\sb1\sl-230\slmult0 \up0 \expndtw0\charscalex102 terjangkau dari beberapa set node lain, mereka\par\pard\ql \li1334\sb0\sl-230\slmult0 \up0 \expndtw0\charscalex105 menghabiskan waktu dan secara bertahap\par\pard\ql \li1334\sb1\sl-230\slmult0 \up0 \expndtw0\charscalex103 meningkatkan perkiraan jarak ke sana, padahal\par\pard\ql \li1334\sb0\sl-230\slmult0 \up0 \expndtw-3\charscalex100 sementara itu mungkin ada routing loop).\par\pard\column \ql \li6343\sb0\sl-276\slmult0 \par\pard\ql \li6343\sb0\sl-276\slmult0 \par\pard\ql \li6343\sb0\sl-276\slmult0 \par\pard\ql \li6343\sb0\sl-276\slmult0 \par\pard\ql \li6343\sb0\sl-276\slmult0 \par\pard\ql \li73\sb161\sl-276\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf5\f6\fs24 REFERENSI\par\pard\ql \li6290\sb0\sl-207\slmult0 \par\pard\ql \li20\sb20\sl-207\slmult0 \up0 \expndtw-1\charscalex100 \ul0\nosupersub\cf16\f17\fs18 [1] http://en.wikipedia.org/wiki/\par\pard\ql \li380\sb0\sl-207\slmult0 \up0 \expndtw-3\charscalex100 Bellman%E2%80%93Ford_algorith.\par\pard\ql \li20\sb4\sl-207\slmult0 \up0 \expndtw-2\charscalex100 [2] http://en.wikipedia.org/wiki/Distance-\par\pard\ql \li380\sb1\sl-206\slmult0 \up0 \expndtw-3\charscalex100 vector_routing_protocol\par\pard\ql \li20\sb1\sl-206\slmult0 \up0 \expndtw-2\charscalex100 [3] http://equatorialmaths.wordpress.com/2009/09/18/bellman-\par\pard\ql \li380\sb1\sl-206\slmult0 \up0 \expndtw-3\charscalex100 ford-algorithm-for-shortest-paths/\par\pard\ql \li20\sb2\sl-206\slmult0 \up0 \expndtw0\charscalex102 [4] Leiserson, Charles. E, \u8220?Shortest Path 2\u8221?, \u8220?Introduction to\par\pard\ql \li380\sb1\sl-206\slmult0 \up0 \expndtw-3\charscalex100 Algorithms\u8221?, 18, 2001.\par\pard\ql \li20\sb2\sl-206\slmult0 \up0 \expndtw-1\charscalex100 [5] Munir, Rinaldi. (2006), \u8220?Diktat Kuliah IF2153 Matematika\par\pard\ql \li380\sb1\sl-206\slmult0 \up0 \expndtw-3\charscalex100 Diskrit Edisi Keempat\u8221?, Program Studi Teknik Informatika,\par\pard\ql \li380\sb6\sl-207\slmult0 \up0 \expndtw-2\charscalex100 Sekolah Teknik Elektro dan Informatika, Institut Teknologi\par\pard\ql \li380\sb0\sl-206\slmult0 \up0 \expndtw-3\charscalex100 Bandung.\par\pard\qj \li20\ri714\sb1\sl-206\slmult0 \up0 \expndtw-2\charscalex100 [6] ranau.cs.ui.ac.id/sda/archive/2006/ShortestPathAdd-2pp.pdf \up0 \expndtw-2\charscalex100 [7] www.personal.kent.edu/~rmuhamma/Algorithms/\par\pard\ql \li380\sb1\sl-206\slmult0 \up0 \expndtw-3\charscalex100 MyAlgorithms/GraphAlgor/bellFordAlgor.htm \par\pard\sect\sectd\sbknone \ql \li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907

\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb0\sl-230\slmult0 \par\pard\ql\li907\sb72\sl-230\slmult0 \up0 \expndtw-3\charscalex100 \ul0\nosupersub\cf1\f2\fs20 MAKALAH IF3051 STRATEGI ALGORITMIK TAHUN 2009-2010 \par\pard\sect\sectd\fs24}