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Washington University in St. Louis Washington University in St. Louis
Washington University Open Scholarship Washington University Open Scholarship
All Computer Science and Engineering Research Computer Science and Engineering
Report Number: WUCSE-2003-75
2003-12-04
Resource Configuration and Network Design in Extensible Resource Configuration and Network Design in Extensible
Networks Networks
Sumi Y. Choi
The goal of packet-switched networks has conventionally been delivering data to users. This
concept is changing rapidly as current technologies make it possible to build network
processing engines that apply intermediary services to data traffic. This trend introduces an
extensive range of ways to develop and operate applications by allowing processing services
customized for applications' needs at intermediate network users, as it can relieve individuals
from the need to acquire, install, and maintain software in end systems to perform required
functions. As such network services become more widely used, it will become increasingly
important for service providers to have... Read complete abstract on page 2. Read complete abstract on page 2.
Follow this and additional works at: https://openscholarship.wustl.edu/cse_research
Part of the Computer Engineering Commons, and the Computer Sciences Commons
Recommended Citation Recommended Citation Choi, Sumi Y., "Resource Configuration and Network Design in Extensible Networks" Report Number: WUCSE-2003-75 (2003). All Computer Science and Engineering Research. https://openscholarship.wustl.edu/cse_research/1121
Department of Computer Science & Engineering - Washington University in St. Louis Campus Box 1045 - St. Louis, MO - 63130 - ph: (314) 935-6160.
This technical report is available at Washington University Open Scholarship: https://openscholarship.wustl.edu/cse_research/1121
Resource Configuration and Network Design in Extensible Networks Resource Configuration and Network Design in Extensible Networks
Sumi Y. Choi
Complete Abstract: Complete Abstract:
The goal of packet-switched networks has conventionally been delivering data to users. This concept is changing rapidly as current technologies make it possible to build network processing engines that apply intermediary services to data traffic. This trend introduces an extensive range of ways to develop and operate applications by allowing processing services customized for applications' needs at intermediate network users, as it can relieve individuals from the need to acquire, install, and maintain software in end systems to perform required functions. As such network services become more widely used, it will become increasingly important for service providers to have effective methods to configure applications sessions so that they use resources efficiently. On the other hand, it is equally important to design such extensible networks properly in order to ensure desirable performance of applications. This dissertation addresses these two key problems that arise in operation and provisioning extensible networks: configuring application sessions and designing extensible networks. First, we present a general method, called layered networks, for the problem of configuring application sessions that require intermediate processing. The layered network method finds optimal configurations by transforming the session configuration problem into conventional shortest path problem. We show, through a series of examples, that the method can be applied to a wide variety of situations. We also discuss how to configure applications that require reserved capacity and propose effective heuristic algorithms that are based on the layered network method. Second, for designing extensible networks, we generalize the constraint-based network design methods originally developed for conventional networks. We show how to incorporate arbitrary requirements that are allowed by extensible networks in a flexible and general way. We also show how to extend the original framework to dimension both processing resources and link bandwidth. These results have been incorporated into software packaged the Extensible Network Planner (XNP).
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Telephone Network
Cellular Network
Overlay Network
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Network Access from homes
Medical facility
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destination
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data decompressed here
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en- crypt
de- crypt
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WXG�K O^M1M1kYBhZ ObWXBhH^U1`ND� �G1BY`�S1Bh`L`RKNJ3W OQWRBhHIU�BY`�HIJLBhKNU?WRKNS�WXH���O^JRS O e BhK�� H^] K�� WXKVU1`RB = khKcU�KVW�� HIJ��n`
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JRKV`RHI@�JRZNKV` � �G�K > ZVHIU�]_HIJLA WRH l ��KNS M1JRHQWXH ZNHIkY` BhU WXG1K @�U1S1KNJLk > BhU�g"U1KVW�� HIJ��n`Vq�O^U1S2H^U1k >
WXG�K khBYU � = OQU1S ��BhS�WXGfBY`dZVHIU1`RBYS1KNJLKNS O `RGPO^JLKNSfJLKN`LHI@1JRZVK^D-��H���K[eIKVJNq�WXG1KCZN@1JLJRKVUnW WXJRKVU1SfBYU
O^M1M�khBhZNOQWXBYHIU1`Vq+MPO^J3WXBYZN@1khO^JRk > BhUfK � WXKNU�`RB = khK U1K[W���H^J��n`Nq$`RG1H���`cApHIJRKCZNHIApM1JLKNG1KVU1`RBmeIK\@1`LK H^]
U1K[W���HIJ�� JLKN`RH^@1JRZVKN`Nq$JRKVon@1BhJLBhU1g `LHIApK U1K[W���HIJ�� U1H S1KV`EWXH M1JLH e�BYS1K M1JLHIgIJRO^A ACH S1@1kYKN`EOQU1S
O^`L`RH ZNBjObWXKNS M1JLH�ZVKN`L`RBhU�g JLKN`RH^@1JRZVKN`ND � G1BYkhK kYBhU � = O^U1S ��BhS�WRG ApKNS1BhOfBh`\`3WXBhkYk�O^U KV`R`RKVU?WXBjOQk
JRKV`RHI@�JRZNK BYU�K�� WXKVU1`RB = khKcU1K[W���H^J��n`Nq U1K�� JRKV`RHI@1JLZNKV` O^JLKcU1KNZVKN`L`XO^J > WXH\MFKNJL]_H^JRA ZV@1`LWRHIApB �NKVS
M1JLH�ZVKN`R`LBhU1g HIJ O^S�e^OQU1ZNKVS2`RKNJ3e BhZNKV`\HIU4U1K[W���H^J�� U�H�S1KV`ND7 �G�KNJRK O^JRK-W�� H = JLH?O^S WXO^`��n`\BYU
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K�� WRKNU1`LBYeIKVk > BhU WXG�Bh`$S1Bh`L`RKNJ3W OQWRBhHIU D+ �G1K�U1K�� W�W�� H `LKNZ[WXBhH^U1`�BYUnWRJRH S1@1ZVK�WRG1KNA6BYUCApHIJRK�S1K[W O^BYk D
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WXKVU1`RB = khK U1KVW�� HIJ��n`VD"��KVJRK^q O^M1M�khBhZNOQWXBYHIU `LKN`L`RBhH^U1` O^JRK\BYU1`LWXO^U1ZVKN`cH^]�U1K[W���HIJ��"O^M1M�khBhZNOQWXBYHIU1`
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U1H S1KN`VD� HpACKVKVW�WRG1KN`LKdU1KVKNS1`VqFW�� HpJRKNon@1BYJRKVACKVUnWR`�AE@1`LW = K�`XOQWRBh`Ll1KNS D$!+BYJR`LWNqPOcJRHI@�WXK�AE@1`3W
= KcS1KVWRKNJRApBhU�KNS�]_HIJ�K OQZ G O^M�M1khBYZ OQWRBhHIU `LKN`L`RBhH^U WRGPOQW�`XObWXBh`3lPKN`�WRG1KcM1JRH ZNKV`R`LBhU1g JRKVo @�BhJRKVACKVU?W
� OQU1SiM*HI`L`RB = k > WXG1K = O^U�S ��BhS�WRGTJLKNon@1BYJRKNApKNU?W��HQ] WRG1K�`RKN`L`RBYHIU D ��KNZVHIU1S q1WRH gI@PO^JRO^U?WXKNK�WRG1KNBYJ
O eQO^BhkhO = BhkYBYW > q JLKN`LHI@1JRZVKN`�AE@1`3W = K�`RKVZN@1JLKNS-]_H^J%WXG1K�S1@1JROQWXBYHIU\H^] WXG1K�`RKV`R`LBhHIU D
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U1KVZNKN`L`XO^J > ]_HIJ$S1B � KVJRKNU?W�O^M1M1kYBhZNOQWXBYHIU1`Nq O^U�S HIU1K�JRHI@�WXBhU�gdApKVWRG1H�SCBh`$`R@ pZVBhKNU?W%]_H^J�O^kYkvO^M1M1kYB �
Z ObWXBhH^U1`ND$ �G1KNJLKdG1O^` = KNKVU OcgIH H�SiS1KNO^k;H^]9JLKN`LK O^JLZ G-HIU ZNHIApM1@�WRBhU1g HIM�WXBhACO^k JLHI@�WRKN`ND�,THI`3W
O^kYgIHIJRBmWXG1Ap`'KNApM1khH > KNBYWRG1KNJ WXG1K�S1BY`LWXO^U1ZNK%e^KNZ[WXHIJ�O^M�M1JRH?OQZ GpH^J+WXG1K�kYBhU ��`3W OQWRK�O^M1M1JLH?O^Z G�� A A � D �G1K BhApM1kYKNApKNU?WXKVS�M1JRH^WRH�ZVHIkh`�BhU1ZVkh@1S1KdWXG1Kp���) M1JLH^WXH ZNHIk � A r�� q'�<��)$! � A t � q;O^U�S )���� � A D � D �G1K�ZVHIApACHIUCgIH?O^kFH^] WRG1K�JLHI@�WXBYU1gEOQkhgIHIJLBYWRG1AC`�BY`$WRH lPU1S WRG1K�HIM�WRBhACO^kPMPOQWRG1`�]_HIJ M*HQWXKNU?WRBjO^k
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O^M1M�khBhZNOQWXBYHIU�`RKV`R`LBhHIU1`dBhU K�� WXKVU1`RB = khKpU1K[W���HIJ��n`NDT!vH^JdOigIBmeIKNU O^M1M1kYBhZNOQWXBYHIU�`RKV`R`RBYHIU q BYW<A O >
U1H^W = K `R@ pZNBYKNU?W<WXHilPU1S O `LG1HIJLWRKN`3W MPObWXG WXH `XOQWRBh`L] > WXG1K M1JLH�ZVKN`R`LBhU1gTJRKVo @�BhJRKVACKVU?W Dp �G1K
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Z OQMPO = kYK U1H S1K^D-� eQO^khBYS JLHI@�WXKQq�G1H���K[eIKVJNq$AE@1`LW BhU1ZVkh@1S�K OQW khK OQ`LWEH^U1K `RK[WcH^]�U1H S1KV` WXGPObW
Bh` Z O^MPO = khK\H^]�WRG1K\M1JRH ZNKV`R`LBhU1g1D ��U HIM�WRBhACO^k JLHI@�WRK\AE@1`LW = K\HIU�K HQ]�WRG1HI`LK e^OQkhBhS JRHI@�WRKN`Vq
��G1KVJRK^q^BhUdO^S1S1BmWXBhH^U�WRH�WRG1K$BhApMPO^ZVW;HQ]1@1`LBhU1g�khBhU ��JRKV`RHI@�JRZNKV`NqIWRG1K BYACM1O^ZVW;H^]�@1`RBYU1g�M�JRH ZNKN`L`RBYU1g
JRKV`RHI@�JRZNKV`�Bh`�OQkh`RH�ZNHIU�`RBhS�KNJRKVS D�!P@1JLWRG1KNJLACH^JRK^qQBhUcO�`RBYWR@POQWRBhHIU ��G�KNJRK WXG1K�M1JLH�ZVKN`L`RBhU�g�Z GPO^U1gIKV`
QWXG�K khBYU � = O^U1S ��BYS�WXG q�WRG1K JLHI@�WXK-`RKNkYKNZ[WXBhH^U4A O > O^kh`LHfU1KVKNS4WXH"JLK��PKVZVW\WRG1K K��*KNZ[W\H^]�WXG�K
eQO^J > BYU1g = O^U�S ��BhS�WRG D�!+BYgI@1JRK A D t `RG1H���`�O^U K ��O^ACM�khK�H^];`L@1Z Gi`RKV`R`RBYHIU1`Vq ��G1KNJLK�ZNHIApM1JRKV`R`LKNSe BhS1KVH-SPObW OiBh`<`RKNU?Wd]_JRHIA O `RHI@�JRZNKpWXHTOTJLKNZNKVBYe^KNJ���G�BhZ G BY`�BhU1ZNO^MPO = kYK H^]�MFKNJL]_H^JRApBhU1g\WXG�K
O^`L`RH ZNBjObWXKNS S1KVZNHIApM1JLKN`R`LBhHIU M1JLH�ZVKN`L`RBhU�g1Dc��KVJRKQq;WRG1K BhU1BmWXBhO^kue�BYS1KNHi`3WXJRKNO^A quZNHIApM1JRKV`R`LKNS =n>
A s � A q?BY`�`RKNU?W$]_JRHIA0WXG1K�`LHI@1JRZVK�OQU1SCBY`�S1KNZVHIApM1JRKV`R`RKVS OQW$O�M1JLH�ZVKN`R`LBhU1g<U1H S1K�KNUCJRHI@�WXK%WXH�WXG�KJRKVZNKVBYeIKVJND�:�KNZNO^@1`RK S1KNZVHIACM�JRKN`L`RBYHIU M1JLH�ZVKN`R`LBhU1g K���MPO^U1S�`�SPOQWXO = O^U1S ��BhS�WRG q*BmW�BY`�M�JRKV]_KVJRJLKNS
WXH MFKNJ3]_HIJRA WXG1BY`�M1JRH ZNKV`R`RBYU1g ZNkYHI`RK�WRH WRG1K�S1KV`LWXBYUPOQWRBhHIU D� �G�K<Z G�HI`RKVUTJLHI@�WXK�OQU1STM�JRH ZNKN`L`RBYU1g
U1H S1K�O^JRK�`LG1H���U =?> WRG1BhZ��EkYBhU1KV`�BhU !+BYgI@1JLK A D t�D+��UpgIKNU1KVJXO^k q?JRHI@�WXBhU�g�ACK[WXG1H S1`�BhUcK ��WRKNU1`LB = kYK
destination
source
compressed video ( ratio of 10 : 1 )
stream sent from source
decompressed video stream takes 10 times
more bandwidth
video decompression occurs here.
de- comp
de- comp
de- comp de-
comp
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U1K[W���HIJ��n`pA @1`LWEWXO �^K\BYU?WXH�O^ZVZNHI@�UnW WXG1K\BYACMPOQZVWdH^]�@1`RBYU1g khBYU � JRKV`RHI@1JLZNKV`Nq�WXG1K BYACM1O^ZVWdH^]
@1`LBhU1g M1JLH�ZVKN`R`LBhU1g JLKN`RH^@1JRZVKN`Nq�WRG1K = O^U�S ��BhS�WRG2e^OQJRBjObWXBhH^U4S1@1K�WXH M1JLH�ZVKN`L`RBhU�g1q�O^U�S HQWXG1KVJ
O^M1M�khBhZNOQWXBYHIU Z GPOQJXO^Z[WXKNJLBh`3WXBhZV`%WXGPObW�O� KVZVW�WRG1K�JRKN`LHI@1JLZNK�`RKVkhKNZ[WXBYHIU D$#�GPO^M�WXKNJL`�rcO^U�STtc`3WX@1S >
ApKVWXG�H�S1`%WRGPOQW�Z OQU = K�O^M1M1kYBhKVSiWRH S1BYe^KNJR`LK OQM1M1khBYZ OQWRBhHIU�`%O^U1S `RBmWX@PObWXBhH^U1`ND
��`�ACKVU?WXBhH^U1KNS qnWXG�K�`RKVZNHIU1SiJLKNon@1BhJLKNApKNU?W�BYU ZNHIU�lPgI@1JLBhU1gcOQM1M1khBYZ OQWRBhHIU `LKN`R`LBhHIU�`�Bh` WRH
gI@POQJXO^U?WXKVK JLKN`RH^@1JRZVKiO eQO^BYkjO = BhkhBmW > D &;K[WE@1`dZNHIU�`RBhS�KNJEOT`RBYWR@POQWRBhHIU ��G1KNJLK WXG�K JRKV`RHI@1JLZNKV`EJRK �
on@1BhJLKNScWXH�ZVHIU�lPg^@1JRK�O^U OQM1M1khBYZ OQWRBhHIUd`RKV`R`RBYHIUpGPO eIK = KNKNUpBhS�KNU?WXBmlPKNS =?> WRG1K�JRH^@�WXBYU1g�ApKVWXG�H�S D
��U H^JRS1KVJdWXHTgI@PO^JRO^U?WXKVKCZVHIU1`RBY`LWRKNU?WcMFKNJL]_H^JRACO^U1ZNKc]_HIJ�WXG�K `RKV`R`LBhHIU q M1JRH^M*KVJdZNO^MPO^ZVBYW > AE@1`3W
= K ACO^BYUnWXO^BhU�KNS OQWpK OQZ G H^]�WXG1K JRKV`RHI@�JRZNKV`p]_H^J WRG1KiS1@1JROQWXBYHIU H^]�WRG1Ki`RKN`L`RBYHIU D2� BhgIUPOQkhkhBYU1g
Bh`�JRKVo @�BhJRKVS WXH MFHIkYk'KNO^Z G JRKV`RHI@1JLZNKE]_HIJ�O e^OQBhkjO = BhkYBYW > O^U1S WXH `RKNZV@1JRKEWRG1KEJLKNon@1BhJLKNS�ZNO^MPO^ZVBYW > D
C� K ��Bhkhk = JRBYK�� > S1Bh`LZN@1`L` M*HI`L`RB = khK ��O > ` WRH BhApM1khKVACKVUnWdWXG1K\`LBhgIU1O^khkYBhU1gTO^U1S"WXG�K JLKN`LHI@1JRZVK
JRKV`RKVJLeQOQWXBYHIU\]_HIJ�K�� WRKNU1`LB = kYKdU1K[W���H^J��n`ND
����� � ��� � �������� � �� ����� ������� ���������� �(�
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ZNJL@1ZNBhO^k*WRHcS1KNkYBYe^KNJRBYU1gEMFKNJ3]_HIJRACO^U1ZVK�gI@PO^JRO^U?WXKVKN`%]_HIJ�O^M1M1kYBhZ ObWXBhH^U1`ND+: > ZNO^JRK[]_@1khk > S�KVWXKVJRApBhU �
BhU�g ��G1KVJRK WRH M1khO^ZNKdJRKN`LHI@1JLZNKN`�O^U1S G1H��0AE@1Z G-Z O^MPOQZNBYW > WRH O^`L`RBhg^U-WXHCK O^Z G�JLKN`RH^@1JRZVK^q HIU�K
Z OQU M1khO^U OiU1K[W���HIJ�� WRGPOQW ��BhkYk�K��*KNZ[WXBYe^KNk > `RKNJ3eIK WRG1KpK���M*KVZVWRKNSfWXJROpZ ��G�BhkhK ApBhU1BYACB��NBYU1g
WXG�KcZNHI`3WdHQ]�S1KVM1khH > ApKNU?W Dc(�KVM*KVU1S1BYU1g\HIU�WXG1K M1@�JRMFHI`RK H^]�WXG�KpU�KVW�� HIJ��vq;WXG1KcZ GPOQJXO^Z[WXKNJLBh` �
WXBYZN`<H^]�O^M�M1khBYZ OQWRBhHIU1`Vq'O^U1S WRG1KCWRJXOpZ M1OQWRWRKNJRU�` H^]�@�`RKNJL`Nq9WRG1KCH^M�WXBYA O^k�S�KN`RBYgIUfACO > e^OQJ > D
�G1KcH = �LKNZVWRBYe^KEBh`�WRH S1KV`RBhg^U O^U1S ZVHIU�lPgI@�JRKcK�� WRKNU1`LB = kYKEU1KVW�� HIJ�� `�WRGPOQW�OQJRKEgI@1O^JXO^U?WRKNKNS WRH
GPO eIKd`R@ pZVBhKNU?W�U�KVW�� HIJ�� = O^U�S ��BhS�WRG�O^U1STM1JRH ZNKV`R`LBhU1gCJRKN`LHI@1JLZNKN`�WXH ApKNK[W�K ��M*KVZVWXKVS WXJROpZ
S1KVA O^U�S1`ND$!+BYgI@1JRK A DEDp`LG1H���`�O U�KVW�� HIJ�� ZVHIApM*HI`LKNSiH^]'l1eIK�kYH�ZNOQWXBYHIU1`�BYU WXG1K�U�HIJLWRG1K O^`3WXKVJRU
Total incoming and outgoing traffic is at most 500Mb/s, each
at New York
500Mb/s at Philadelphia
800Mb/s
800Mb/s
500Mb/s 500Mb/s
200Mb/s
200Mb/s
200Mb/s 200Mb/s
300Mb/s
300Mb/s
200Mb/s at Indianapolis
300Mb/s at Detroit
300Mb/s at Cleveland
Traffic required for link ( Philadelphia, Indianapolis )
To satisfy the traffic expectation at all cities, 800Mb/s required
for ( New York, Cleveland )
!+BhgI@�JRK A DED � � ��O^ACM�khK�H^] U1KVW�� HIJ��\S1KN`LBhgIU
��U�BYWXKVSp� W ObWXKN`VD9��UEWXG�Bh`+U�KVW�� HIJ��vq?WXG1K�H^@�WXgIH^BhU1g�O^U1ScBhU�ZNHIApBhU1g�WXJROpZ%Bh`+OQW�ApHI`LW B^sIs�, = �Q`OQW��K��4�$HIJ��pO^U1S )�G1BhkhO^S1KNkYM1G1BhO�qntIsIs , = �Q`�OQW%(�K[WXJLHIBYW O^U1S #�khK[eIKNkhO^U1S q�O^U1S r^sIsE, = �Q`%ObW
N��U1S1BhO^UPO^MFHIkYBh`ND H O^ZNZVHIACApH SPOQWXK�OQU > WRJXOpZdWRGPOQW�H = K > `�WRG1KN`LK ZNH^U1`LWRJXO^BYUnWR`NqFWXG1K<U1KVW�� HIJ��
AE@1`3W�GPO eIK = O^U1S ��BYS�WXGi]_HIJ�K O^Z GTkhBYU � O^`�`RMFKNZVBYlPKVS-BYUiWRG1K�lPgI@1JLK^qFO^`R`L@1ApBhU1gcWXG1OQW�WXJXO CZ�BY`
JRH^@�WXKVSTWXG�JRHI@1g^G-`RG�HIJLWRKN`LW�MPOQWRG1`ND���@1J�O^M1M�JRH?O^Z G-K�� WXKVU1S1`�WRG1Bh`�ZNH^U1`LWRJXO^BYUnW � = OQ`RKNSTU1KVW�� HIJ��
S1KV`RBhg^UTApKVWRG1H�S�HIkhHIg > � A Q �uWRH K�� WXKVU1`RB = khK�U1K[W���HIJ��n`ND#�H^U1`LWRJXO^BYUnW � = OQ`RKNS S1KV`RBhg^UTH^] ZNH^Une^KNU?WXBYHIUPO^kuU�KVW�� HIJ��n`�`3W O^J3WX` ��BYWRG O `LKVW�H^] U1KVW�� HIJ��
khH Z ObWXBhH^U1`Nq'HIJ `LBYWRKN`Nq9O^U1S O-`LKVWEHQ]�WXJXO CZCZNHIU�`LWXJRO^BhU?WR`ND ��UfWRG1K `LBhApM1khKV`LWdZ O^`LK^q9WXG�K WXJROpZ
ZNH^U1`LWRJXO^BYUnWR`c`RBYACM1k > M1kjO^ZVK @1M1MFKNJ = HI@1U�S1` HIUfWXG1KiOQACHI@�UnWEH^]�WXJXO CZ WRGPOQWcZNO^U HIJRBYgIBhU1OQWXK
HIJ�WXKVJRApBhUPOQWRKpOQW<K O^Z G"`LBYWXK�� A C�q A?N q r^s�q+r A � q9O^`<K���KNApM1kYBYlPKVS BhU !+BYgI@1JRK A DED1D ��U"OQS1S1BYWRBhHIUWXH\`LBhApM1khK<BhU�gIJRKV`R` �bKNgIJLKN`R`�ZVHIU1`LWRJXO^BYU?WX`Nq U1KVW�� HIJ��-S1KN`LBhgIU1KVJR`�ACO > `LM*KVZNBY] > ZNHIU�`LWXJRO^BhU?WR`�WXGPObW= HI@1U1S WRG1K O^ApHI@1U?W�H^]�kYHIU1g S1BY`LWXO^U1ZNKEWRJXOpZEH^J�khBYACBmW�WRG1K WRJXOpZ = KVW�� KNKNU MPO^BYJR`�HQ] `LBYWRKN`ND
!PHIJ$K���O^ApM1khKQq � K�ACO > O^S�S\O MPO^BYJ���BY`RK�WXJXO CZ�ZNHIU�`LWXJRO^BhU?W WXHc!+BYgI@1JLK A DEDdWRGPOQW�JRKN`3WXJLBhZVWR`�WXG�KWXJROpZ ]_JRH^A �K��6�$HIJ�� WRH ��U1S1BhO^UPO^MFHIkhBY`�WXH = K khKV`R` WRGPO^UfH^JEKNon@PO^k$WXH A sIs�, = �b`ND� �G1BY`JRKVS1@1ZVKN` WRG1K = OQU1S ��BhS�WXG4U1KVKNS1KVS4]_JRHIA �K�� �$HIJ��fWXH"#�kYKVe^KNkjOQU1S WXHQ^sIs , = �Q`CBhU KNO^Z GS1BYJRKNZ[WXBYHIU D� �G�KcgIKNU1KVJXO^k;]_HIJLA H^]$OpWXJXO CZ ZNHIU1`3WXJRO^BhU?W�BY`�O = HI@1U�S�HIU-WXG�K WXJROpZ = K[W���KVKNU
O^U > W�� Hi`R@ = `RKVWR`�H^]$`RBYWRKN`VDE��BYe^KNU O `RK[W�H^]$ZNHIU1`3WXJRO^BhU?WX`Vq WXG�KcS1KN`LBhgIU�M1JLH = kYKNA BY`�WRH lPU1S O
khKNO^`LW ��ZVHI`LW<U1K[W���HIJ�� ZNHIU�l1gI@1JXObWXBhH^U BYU ��G1BhZ G WXG1KpkhBYU �-ZNO^MPO^ZVBYWXBYKN`�KVU1`R@1JLKCWRGPOQWdO^U > WXJROpZ
ZNH^U�lPgI@1JROQWXBYHIU O^khkYH���KVS =?> WRG1K�ZNHIU�`LWXJRO^BhU?WR`�ZNO^U = K�GPO^U�S1khKVS D
� K�`RG�H � G1H�� WXG1BY`%HIJRBYgIBhU1O^kP]_JXO^ApK�� HIJ��pZ OQU = K�g^KNU1KVJXO^kYB �NKVS WXHcGPOQU1S1khK�WXG1K�ZVHIU�lPg �
@1JROQWXBYHIUCHQ] M1JLH�ZVKN`R`LBhU1g JRKN`LHI@1JLZNKN`�O^U1S kYBhU � = O^U1S ��BhS�WRG BhUpK�� WXKVU1`RB = khK�U1K[W���HIJ��n`ND$ H = JRBYK�� >
BhkYkh@1`3WXJROQWXKEWRG1K S1KV`RBYgIUfH^]�K � WXKNU�`RB = khK U�KVW�� HIJ��n`Nq�kYKVWd@1`dWXO �^K O^U K �1OQACM1kYK^Di��U"!+BYgI@1JLK A D B�q� K�`RG1H�� O^UCK�� WXKVU1`RB = khK�U1KVW�� HIJ�� ��BYWRGCWXG�K�`XOQACK�WXHIMFHIkhH^g > O^` BhU ! BhgI@1JLK A D D O^U1S ��BmWXGCW�� HM1JLH�ZVKN`R`LBhU1gdU1H S1KN` � G1BYgIG1kYBhgIG?WXKVS �[D'��UCWRG1Bh`$K�� WRKNU1`LB = kYK�U1K[W���H^J��vq � K�ZVHIU1`LBhS1KVJ�O�e�BYS1KNH�WXJRO^U1` �
ApBh`R`LBhHIU O^M1M1kYBhZ ObWXBhH^U JRKVon@1BhJLBhU1gES�KNZNH^ACM1JLKN`L`RBhH^U M�JRH ZNKN`L`RBYU1g BhU WRG1K�U1KVW�� HIJ��\O^`�BhU?WRJRH S1@1ZNKVS
BhU/!+BYgI@1JLK A D t�D/(�@1JRBYU1g WXG1Ki`LKN`R`LBhHIU�`CZVHIU�lPgI@�JRKNS ]_HIJcWXG�Bh` O^M1M�khBhZNOQWXBYHIU q9WRG1KiZNHIApM1JRKV`R`LKNSe BhS1KVHc`LWRJRK OQA Bh`�`RKNU?W�]_JLHIA OE`LHI@1JLZNK�O^U1SiS1KVZNHIApM1JLKN`R`LKNS HIU WXG�K�JRHI@�WRK�WXH OEJLKNZVKNBYe^KNJVD (�@�K
WXH\WRG1KcZNHIApM1JLKN`R`LBhHIU JROQWXBYH1q ��G1BYZ G BY`�O^`L`R@1ApKNS WXH = K A s � A BhU WXG�Bh`�ZNO^`RKQq'S1OQW O = O^U�S ��BhS�WRGZ GPO^U�gIKN`�S1@1JLBhU1gcWXG�K<WRJXO^U1`LACBY`R`LBhHIU D� �G�KdkYBhU �pZ O^M1O^ZNBmW > OQW�K O^Z GTkhBYU �CA @1`LW�WXG�KNU = K�S1KVWRKNJ �
ApBhU1KVS =?> ZNHIU1`LBhS1KVJXOQWRBhHIU H^]%WRG1Bh`dO^M1M1kYBhZNOQWXBYHIU Z GPO^JXOQZVWXKVJRBY`LWXBYZ^Di �G1KCM1JRH ZNKV`R`RBYU1g JLKN`RH^@1JRZVKN`
A s
de- comp
de- comp
500Mb/s at New York
500Mb/s at Philadelphia
200Mb/s at Indianapolis
300Mb/s at Detroit
300Mb/s at Cleveland
Here, decompression expands data bandwidth by 10 times. 10 times more bandwidth is needed on link used after
decompression.
Compressed video traffic must be decompressed either at Cleveland or Philadelphia
!+Bhg^@1JRK A D B � � ��O^ApM1khK�H^] U1K[W���HIJ��\S1KN`LBhgIU ��BYWRGiM1JRH ZNKV`R`RBYU1g
O^U1S WRG1KNBYJ%Z OQMPO^ZNBmW > A @1`LW�O^kY`RHEZVHIApM1k > ��BYWRG WXG1K�S�KNZNH^ACM1JLKN`L`RBhH^U `LM*KVZNBmlPZ OQWRBhHIU O^U1S\WXJROpZ
K���MFKNZ[W OQWRBhHIU D
: KNZ OQ@1`RK%WRG1K�JLKN`RH^@1JRZVKN`9U1KVKNS1KVS =?> O�U1KVW�� HIJ�� O^JRK$G1BYgIG1k > S�KNMFKNU1S1KVU?W�HIU WRG1K�Z GPOQJXO^Z �
WXKVJRBY`LWXBYZN` H^]1WXG�K�O^M1M1kYBhZNOQWXBYHIU1`Nq � K%BhU?WXJLH�S�@1ZNK�O�gIKNU�KNJXOQk�ApKVWRG1H�Sd]_HIJ S�KN`RZVJRB = BhU1g�WXG1K%JLKN`LHI@1JRZVK
JRKVon@1BhJLKNApKNU?WX`�H^] O^M1M�khBhZNOQWXBYHIU-ZVkjO^`L`RKV`dOQU1S `RG1H�� G�H �0WXG�KN`RK ZNO^U = Kc@1`LKNS BhU WRG1KcU1KVW�� HIJ��
S1KV`RBhg^UTM1JLH�ZVKN`L`ND � K�GPO eIK<BhU1ZVHIJRMFHIJROQWXKVSiWRG1K<ACK[WXG1H S1`�S1KVe^KNkYHIM*KVS ]_H^J�K � WXKNU�`RB = khK�U1KVW�� HIJ��
S1KV`RBhg^UTBYUnWRH O `RHQ] W��%O^JLKdM1O^Z��bO^gIK<Z O^kYkhKNS\WRG1K<� � WRKNU1`LB = kYK �KVW�� HIJ�� )�kjO^U�U1KNJ � 8��)��[q ��G�BhZ G
Bh` = O^`RKVS-HIUTO^U K O^JLkhBhKVJNq�@1U1M1@ = khBh`LG1KNSiWXH HIk ]_HIJ�S�KN`RBYgIU1BYU1g ZNHIU?eIKVU?WXBhH^UPO^k;U1KVW�� HIJ�� ` � r^r�� D 'H
S1KVACHIU�`LWXJROQWXKEWRG1K @�WXBYkhBmW > HQ] WRG1KN`LKpApKVWRG1H S1`Nq � KCBYU1ZNkY@1S1KEK ��O^ACM�khKN`�HQ]�G1H�� 8��) Z O^U = K
@1`LKNSTWRH S1KN`LBhgIU JRKNO^k U1K[W���HIJ��n`ND
����� � ��� ����� ��� �$� �%� � !���� !#����
#�GPO^M�WXKNJ�rpS1KV`RZVJRB = KN`�JRKV`RHI@1JLZNKdZNHIU�l1gI@1JXObWXBhH^UTApKVWRG1H�S�`�]_HIJ�O^M1M�khBhZNOQWXBYHIU1`%WRGPOQW�JRKNon@1BYJRK<BhU �
WXKVJRApKNS1BhOQWXKCM1JRH ZNKV`R`LBhU1g1D�� K\M1JRKV`RKVUnWpOQU"K�pZNBYKNU?W `RHIkY@�WXBYHIUfZNO^khkYKNS WRG1K������ ������� ���������bq
O^U1S-`RG1H�� BYWX`�O^M1M1kYBhZNO = BhkYBYW > O^U1S `LZ O^khO = BhkYBYW >\=?> S1KN`LZNJLB = BYU1g eQO^JRBYHI@1`�`RBYWR@POQWRBhHIU1` ��G1KVJRKEWXG�K
ApKVWXG�H�ScZNO^U = K�O^M�M1khBYKNS D+#�GPO^M�WRKNJ$t�K�� WRKNU1S1`�WRG1K�JRKN`LHI@1JLZNK�ZNHIU�lPgI@1JROQWXBYHIUEM1JLH = khKVA WRH�U1KVW �
� HIJ��n` ��BmWXG K ��M�khBhZVBYW khBYACBmWX`�HIU JLKN`LHI@1JRZVK�Z OQMPO^ZNBmW > D9� K�BhkYkh@1`3WXJROQWXK�WXG�K�BhU?WRJXO^Z[W O = BYkhBmW > H^]uWXG�K
AOAM1JLH = khKVA ]_HIJ�gIKNU�KNJXOQk ZNO^`RKV`EO^U1S S1KN`LZNJLB = K G1KV@1JRBY`LWXBYZ ACK[WXG1H S1` ��G1BhZ G M*KVJL]_HIJLA K��*KNZVWRBYe^KNk >
BhUiApHI`LW�M�JXO^Z[WXBhZNO^k `LBYWX@1OQWXBYHIU1`ND
#�G1O^M�WXKVJ DcBhU?eIKV`LWXBYg?OQWRKN`%WXG�K�M1JRH = khKNA H^]'S1KN`LBhgIU�BhU1gcK ��WRKNU1`LB = kYK�U1KVW�� HIJ�� `�WXHc`ROQWXBY`L] >gIBmeIKNU OQM1M1khBYZ OQWRBhHIU�`+O^U�SEWXJXO CZ�MPOQWRWRKNJLU1`ND9��] WXKVJ9K���KNApM1kYBY] > BhU1g�WXG1K�M1JRH = khKNA0BhU `RBhApM1kYK^qIOQU1S
> K[W9JLK O^kYBh`LWRBhZQq `RBYWR@POQWRBhHIU1`Vq � K$S1KN`LZNJRB = K�O�` > `LWXKVA ObWXBhZ O^U1SdM1JXOQgIA ObWXBhZ9O^M1M1JLH?O^Z G WRH�S1KV`RBYgIU1BhU�g
K�� WRKNU1`LB = kYK$U�KVW�� HIJ��n`NqIO^U1S<BhkhkY@1`LWRJXOQWRK+WXG�K OQkhgIHIJLBYWRG1ACBYZ ApKVWRG1H S1`;@1`RKVS BhU�WRG1K�S1KN`LBhgIU<M1JRH ZNKV`R`VD
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t d
t d
t d
s
c
b a d
t c
t d
decompression node for all receivers
compression node for all receivers
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t d
t d
s t c
c
b a d
t d
t c
t d
decompression node for receiver c and d
compression node for all receivers
decompression for a and b
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K OQZ GpJLKNZVKNBYe^KNJVD���H�� KVeIKVJNq BhUcS1H^BhU1g�`LH1q � K�khHI`LK�WXG�K�HIM1MFHIJLWR@1U1BYW > WRH�`RGPO^JLK�JRKV`RHI@1JLZNKV`$JRO^Bh`LBhU1g
WXG�K�H eIKVJXO^kYkvZNHI`3W D���U1`3WXK OQS q � K�ZNO^U S1BYJRKVZVWXk > lPU1S OdAE@1kmWXBYZ O^`3W�ZNHIU�l1gI@1JXObWXBhH^U BhU WXG�K�khO > KNJLKNS
U1K[W���HIJ��vq ��G1BhZ G Bh`�ZNH^U1`LWRJR@1Z[WXKNS BhU WXG1K `XOQACK �%O > O^`�]_HIJ�@1U1BYZ O^`3W `LKN`L`RBhH^U1`ND\! BhgI@1JLKCr�D A t`RG�H ��`�WXG1K<kjO > KNJRKVS U1K[W���HIJ��vD� HCZNHIU�l1gI@1JRK<WXG1K<`RKV`R`LBhHIU q � K<lPU�S�OpA @1kYWRBhZ OQ`LW�WXJLKNK<JRH H^WXKVS
OQW 6 @%O^U1S WRKNJRApBhU1OQWXBYU1g<OQW�� B q <4B q \4B�O^U1S 8 B%BYU WXG�K�kjO > KNJRKVS U1K[W���HIJ��vD �G1KVU q � K�M1JLH �LKNZ[W�BYWWXH<WXG1K�HIJLBhgIBYUPO^k1U1K[W���H^J��pgIJXO^M�G BhU WXG�K�`XOQACK �%O > O^`$]_HIJ�@1U1BhZNO^`LW `RKV`R`LBhHIU1`VD� �G1K�M1JLH �LKNZ[WXBYHIU
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KNon@1BmeQO^khKVUnW�AE@1kmWXBhZNO^`LW�`LKN`R`LBhHIU ��BYWXG-M1JRH ZNKV`R`RBYU1g BYUTWXG�K U1K[W���HIJ��Tg^JXO^M1G D� �G1K kjO > KVJRKNS-U1KVW �
� HIJ��iApKVWXG�H�STO^g?O^BYUTkYKVWR`�@1`�G1BhS�K�WRG1K M�JRH ZNKN`L`RBYU1g JLKNon@1BhJLKNApKNU?W ��BmWXGiWXG1KdgIJXOQM1GTWRJXO^U1`3]_HIJ �
ACOQWXBYHIUiO^U1SikhK[WX`�@1`�`RH^kYeIK�WRG1K�M1JRH = khKNA O^`�OcZNHIU?eIKVU?WXBhH^UPO^k;AE@1kmWXBhZNO^`LW%ZNHIU�l1gI@1JXObWXBhH^U D
! BhU1S1BYU1gdWRG1K�kYK O^`3W�ZNHI`3W�ZNH^U�lPgI@1JROQWXBYHIU BY`�ApHIJRK�ZNHIApM1khK �p]_HIJ�AE@�kYWXBYZ O^`3W�`LKN`L`RBhH^U1`ND$��U
] O^Z[W qQWRG1K%AE@�kYWXBYZ O^`3W'JRHI@�WRBhU1g�M1JRH = khKVA0BY`+KVo @�BYeQO^khKVU?W+WXH�WXG1K � � ��GPOQJRS � WXKVBhU1KVJ+WXJLKNK�M�JRH = kYKNA
BhU2g^JXO^M1G�`ND �G�K �nWXKNBYU1KNJCWXJRKVK M1JRH = khKNA GPO^` = KNKVU `3WX@1S�BhKNS K ��WRKNU1`LBYe^KNk > ]_HIJ @1U1S�BhJRKVZVWRKNS
gIJRO^M1G1`Vq�O^U1S WRG1KNJLK\O^JRKC`RK[eIKNJRO^k�O^M1M�JRH ��BhACOQWXBYHIU ApKVWRG1H S1`d]_HIJdBYWNq ��BYWRG WXG�K = KV`LWcApKVWRG1H S
�nU1H���U G1O e BYU1g O � HIJL`LW���Z O^`LK M*KVJL]_HIJLA O^U�ZNKcJXObWXBhH H^] A D BOB � rOQ � Dc��H � KVe^KNJVq'WRG1HI`RK ApKVWRG1H�S�`
t A
a 2
d 2
c 2
b 2
1
2
1
1
3 2
1
1 1
2
1
2 4
2
2
6 4
2
2 2
4 2
2
3 3
2 1
2
t c t c s 0
t d t d
t d t d 1
1
2 4
2
2
6 4
2
2 2
4 2
2
!+BYgI@1JLK�r�D A t � &;O > KNJLKNSTU1KVW�� HIJ��\]_HIJ�A @1kYWRBhZ OQ`LW
Z OQU1U1H^W = K�gIKVU1KNJRO^khB��NKNS ]_HIJ S1BYJRKNZ[WXKVS2gIJXO^M�G1`ND ��U1k > BhU2JLKNZVKNU?W > KNO^JR`iGPO^`CWXG1K�S1BYJRKVZVWXKVS
� WRKNBhU�KNJ WXJLKNK�M1JLH = khKVA = KNKVUd`3WX@1S1BYKNS qbO^U�S<]_K��fO^M�M1JRH ��BhACOQWXBYHIU�ApKVWRG1H�S�`uK���Bh`3W D' �G1K ApKVWRG1H S
M1JLKN`RKVU?WXKNSiBYU � r C � g^BYeIKV` WRG1K�JXObWXBhH<H^] r��7BYUCWXBYACK � � � B <�� � � � � q ��G1KVJRK �CBY`$WRG1K�Un@1A = KNJ H^]JRKVZNKVBYeIKVJR`Vq�� BY`�O�ACKNO^`R@�JRK�H^] WRG1K�OQ` > ACApKVWRJ > HQ] WXG�K�HIM�WXBhACO^kv�nWXKNBYU1KNJ�WXJLKNKQq�O^U�S < � � � � BY`OcWX@1UPO = khK�eQO^JRBhO = kYK�BhU\WXG�K O^kYgIHIJLBYWXG�ATD ��U1H^WRG1KNJ�`RK[W�HQ]+ApKVWRG1H�S�`NqPS1KV`RZNJLB = KNSTBhU � r N � qvgIBmeIKV`WXG�K<JROQWXBYHcH^] � � � A � � >�� � BhU\WRBhApK � ��� � � � � B � �[qPgIBmeIKVU-O^U > ��� A D
��U�]_HIJ3WX@1UPObWXKNk > q WXG1K�JLKN`L@1kYWR`�]_HIJ�S�BhJRKVZVWRKNS\gIJRO^M1G1`�O^JRK�U�H^W�O^M�M1JRHIM�JRBjObWXK�]_H^J�S > UPO^ApBhZ
`RKV`R`LBhHIUEZVHIU�lPg^@1JXOQWRBhHIU�`Nq^`LBhU1ZVK WRG1KNBYJ WXBYACK�ZVHIACM�khK���BmW > Bh`'K���ZNKV`R`RBmeIKQD�� K�`L@1gIgIKV`LW W���H�`LBhApM1khK
G1KV@1JRBY`LWXBYZiACK[WXG1H S1` ��G1BhZ G OQWLWXKNApM�W WXH lPU1S O gIH�H S ZNHIU�lPgI@1JROQWXBYHIU D ��BmeIKNU O AE@1kYWRBhZNO^`LW
gIJLHI@1M ��G1BhZ G BY`cZNHIApM*H^`RKNS H^]�O `RH^@1JRZVK-O^U�S/A @1kYWRBhM1kYKCJLKNZNKVBYe^KNJR`Vq WRG1KiACK[WXG1H S1` � HIJ��"OQ`
S1KV`RZNJLB = KNS = KVkhH���D
� �G1K2���I��-?�?� ��� TI� �� � -L�b� 9 �R��'�58 l1JR`LWdlPU1S1`dWXG1K `LG1HIJ3WXKN`3WcMPOQWRG WXJLKNKCBhU WRG1K khO > KNJLKNSU1K[W���HIJ��iJRH H^WXKVS OQW�WXG�Kd`LHI@1JRZVK^D���W�WXG1KVU-K ��WRJXO^Z[WX`�Op`L@ = WXJLKNK<]_JRHIA WRG1Kd`LG1HIJ3WXKN`3W�MPObWXGiWXJRKVK
`RH WXG1OQW�WXG1K�`L@ = WXJLKNK<ZNHIU?WXO^BhU1`�HIU�k > WRG1K�MPOQWRG1`�WXGPOQW�kYK O^S\WRH WRG1K�JRKVZNKNBmeIKVJR`ND
� �G1K 9 +I�@�?�� ���?�bT �?-.�b�2�Y+'*,9 � 4 �?� �.�@� 4 9 �R��I� 8 BYU1ZNJLKNApKNU?W O^kYk > ZVHIU1`3WXJR@�ZVWX`�OdAE@1kYWRBhZNO^`LWWXJLKNKbU<qI`3W O^J3WXBhU�g ��BYWRG U#� � � 6�� @ � � � O^U1S O�`LKVW�� q ��G�KNJRK26�Bh` WXG1K�`LHI@1JRZVK�O^U1S�� ZNH^UnWXO^BhU�`WXG�K�JLKNZVKNBYe^KNJL`ND���W�JRKVM*KNOQWX`�WRG1K�]_HIkhkYH ��BYU1g�`3WXKNMp@1U?WXBYk�WXG�K�`LKVW�� Bh`�KNApM�W > D�!+BhU�SEWXG1K�JRKVZNKVBYeIKVJ8 L � WXGPOQW<BY`�U1K O^JLKN`3WdWRH]U<D �G1KpS1Bh`3W O^U�ZNKc]_JRHIA U WXHC8 Bh`�ACKNO^`R@�JRKNS O^`�WXG�Kp`LG1HIJ3WXKN`3W
t?rMPOQWRG = KVW�� KNKVU O^U > U1H S1K<BhUZU7WXH 8PD �G�KNU q*O^@1gIApKNU?W�WXG�K�WRJRKVK�U7WRHCBYU1ZNkY@1S1K�WRG1Kd`LG1HIJ3WXKN`3WMPOQWRG ]_JLHIA U WXHcWXG�K<`LKNkYKNZVWRKNSTJRKNZVKNBmeIKNJ#8PqPO^U1S JRKVACH e^K 8 ]_JRHIA � D
� K ZNO^U e BhK�� WRG1KN`LK-W�� H"G1KN@1JLBh`3WXBhZV` O^`CK�� WXJLKNApK Z OQ`RKN` H^]<O ApHIJRKTgIKNU�KNJXOQk�O^kYgIH�
JRBmWXG1A D< �G1K gIKNU1KVJXO^k9O^khgIH^JRBYWRG1A Bh`�O\ApH�S�BYlPZNOQWXBYHIU-H^]�(�B ���n`3WXJXO � `�OQkhgIHIJLBYWRG1ATD���] WXKNJ�`3WXKVM1`
�+@ r(�+@ t �+@H! ! ! HQ]�(�B ���n`LWRJXO � `EO^kYgIHIJLBYWXG�ATq � K\JRKN`LKVWEWRG1K S1BY`LWXO^U1ZNKCe^OQJRBjO = khK 8 � O ��WRH �NKVJRH1q+]_H^J
KVe^KNJ > eIKNJ3WXK � WXGPOQW�BY`�HIU O^U > H^]$WXG�KcMPOQWXG�`�WRGPOQW�ZVHIU1U1KVZVW�WXG1K `LHI@1JRZVKcWXH WXG�KpJLKNZVKNBYe^KNJL`dBYU
WXG�K M1O^JLWRBjO^k�WRJRKVKTZVHIU1`LWRJR@1Z[WXKVS `RH ] O^JND/!PHIJcKNO^Z G H^]�WXG�K � = HI@1U�SPO^J > eIKNJ3WXBYZNKN` � O WRGPOQW BY`ZNH^U1U1KNZ[WXKVS WXH\O^U > eIKVJLWRK��-BhUTWRG1K ZVHIU1`3WXJR@�ZVWXKVS MPOQWXG WXJLKNK^q ��KEO^kh`LH khK[W 8 � O�� = K<WRG1K kYKNU1g^WRGH^]�WXG1K `RG1H^JLWXKV`LWCKNS1g^KTZVHIU1U1KVZVWXBYU1g O WXH `RHIApK\eIKNJ3WXK � ��BmWXG/S1Bh`3W O^U1ZVK\e^OQkh@1K s�D �G1K W�� H
G1KV@1JRBY`LWXBYZN`�ZVHIJRJLKN`RMFHIU1S�WRH `LKVWLWXBhU�g �>� � O^U1S �>� A q JLKN`RMFKNZ[WXBmeIKNk > DE��U?WRKNJRApKNS�BjOQWRKEe^OQkh@1KV`H^] � > BYKNkhSiOQkhgIHIJLBYWRG1AC` H^]'e^OQJ > BhU1gcWRBhApK�ZNHIApM1kYK���BYW > O^U1Sie^OQJ > BhU1g `LHIkh@�WRBhHIU\on@POQkhBYW > D
��`%O^UC@1M1MFKNJ = H^@1U1S HIUpWXG1K�ZNH^`LWX` H^] A @1kYWRBhZ OQ`LW�WXJLKNKN`Vq � K�@1`LK�WRG1K�`L@1A H^] WRG1K�ZVHI`LWR`
H^]PWRG1K%`RG�HIJLWRKN`LW9MPOQWXG�`+WXGPObW9ZNH^U1U1KNZ[W�WXG1K�`RHI@1JLZNK�WRH�WXG�K%JRKVZNKNBmeIKVJR`ND� �G�Bh`+`L@1A JLKNM1JLKN`LKNU?WX`�WXG�K
ZNH^`LW�H^]$ZNH^U�lPgI@1JLBhU1giAE@�kYWXBYZ O^`3W�`LKN`R`LBhHIU�`<`LBhApM1k > =?> BYU1S1KNMFKNU�S1KNU?W<@1U1BYZ O^`3W�ZNHIU�lPgI@1JROQWXBYHIU1`ND
: > ZNHIApMPO^JLBhU1g�AE@�kYWXBYZ O^`3W WRJRKNK\ZVHI`LWR`cWXH WXG�K @�M1M*KVJ = H^@1U1S q � K ApK OQ`R@1JLK WXG1K = KNU1K[l1W H^]
JRKV`RHI@�JRZNK<`RG1O^JRBYU1gpO^ACH^U1gcAE@1kmWXBhM�khK�JLKNZVKNBYe^KNJL`ND
s
3
2
2
source
receivers
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s
3
2
2
tree cost = 5
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s
3
2
2
tree cost = 4
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!+BYgI@1JRK%r�D A D � #�HIACM1O^JRBY`RHIUEHQ]PWXG1K%WRJRKNK�ZNHI`3WX`�JRKV`R@1kmWXBYU1g�]_JRH^A0WRG1K�G1KN@�JRBh`3WXBYZ�ApKVWXG�H�S1`Vq ��G1KNJLKWXG�KpJLKN`L@1kYW<H^] WXG1K `RG�HIJLWRKN`LWdMPOQWRG WRJRKVKCApKVWRG1H�S ZVHI`LWR`dkYKN`R`�WRGPO^U WRG1K AE@1kmWXB ��`LWRKNM WXJLKNKCO^@1g�ApKNU?W OQWRBhHIU
� G�BhkhK WRG1K W�� H G1KV@1JRBY`LWRBhZ\ApKVWXG�H�S1`cWXO �^K O^S�eQO^U?WXO^gIK\H^]�JRKV`RHI@1JLZNKV`C`LGPO^JRKVS OQACHIU�g
S1B � KVJRKNU?W�JRKVZNKNBmeIKVJR`�BYUTJLKNS1@�ZNBhU�gCWXG�K<WRH^W O^kuZVHI`LW�H^]+AE@1kYWRBhZNO^`LW�WRJRKNKV`NqFBYW�Bh`�@1U�ZNkhKNO^J ��G1BhZ GTH^]
tIt
s
2 2
source
3 2 2
receivers
� ��� � �0��� �$�
s
2 2
3 2 2
tree cost = 8
� ( � '� �$��%����� & �A��' �%$����,-�0�%'� �
s
2 2
3 2 2
tree cost = 9
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WXG�K W���H ApKVWRG1H�S JRKNS�@1ZNKV`pZVHI`LWEACHIJLK^D���Uf] O^Z[W q�U1KVBYWRG1KNJEHQ]�WXG1KVA Bh` O^k���O > ` = K[WRWXKVJ WXG1O^U
WXG�K H^WRG1KNJVq O^`�`RG1H���U =?> WRG1K K ��O^ACM�khKN`�BhU-!+BhgI@�JRK r�D A D O^U1S !+BhgI@�JRK r�D A B�D�!+BhgI@�JRK r�D A D � O �`RG�H ��`%O U1KVW�� HIJ�� O^U�S\Od`LBhU1gIkYK���`RHI@1JLZNK�AE@1kYWRBhZNO^`LW$gIJLHI@1MCWRH = K�ZNH^U1U1KNZ[WXKVS D$!+BhgI@�JRK�r�D A D � = �O^U1S ! BhgI@1JLKir�D A D � Z��d`LG1H�� WRG1K\AE@1kmWXBhZNO^`LW<WXJLKNKV`pH = W O^BYU1KNS =n> WXG1K W�� H G1KN@�JRBh`3WXBYZN`ND ��KVJRKQqWXG�K�WRJRKVK<H = W O^BYU1KNS =?> WXG�K<`LG1HIJ3WXKN`3W�M1OQWXG\WXJLKNK<ACK[WXG1H SiGPO^`�Oc`RACO^khkYKNJ%ZVHI`LWND ��UiWXG�K<HQWXG1KVJ
GPO^U�S q�!+BYgI@1JRK r�D A B `LG1H���`EWXG1KCH^WXG�KNJ ZNO^`RKQq ��G1KNJLK WXG�KCWXJLKNKCH = W OQBhU1KVS =?> WRG1K AE@�kYWXB ��`3WXKNMWXJLKNK<O^@1g^ACKVUnWXOQWXBYHIU\ApKVWXG�H�SiGPO^`�Oc`RACO^kYkhKNJ�ZNHI`3W D
'H KVeQO^kY@POQWXK�WXG1K�G1KV@1JRBY`LWRBhZ�ApKVWRG1H�S�`Nq � K�M*KVJL]_HIJLACKVSiOE`RBYAE@1kjObWXBhH^U `LWR@1S > HIU OEU1KVW �
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= O^U�S ��BhS�WRG =n> A s WXBYACKV`ND���U2WXG1K l1gI@1JRKQq � K `RG1H�� WXG1K = O^U1S ��BYS�WXG O eQO^BhkhO = khKTOQW\KNO^Z GkhBYU �/BhU @1U1BmWX`\H^]E, = �Q`VD �H^WRK^q�G�H � KVe^KNJVq�WXGPOQW\WRG1K khKNO^`LW ��ZNH^`LWiMPOQWRG S�H�KV`\U1H^W M1JRH e BhS�KKNU�HI@1gIG Z O^M1O^ZNBmW > D ,TKNO^U ��G1BhkYK^q WRG1K H^WXG1KVJ�ZNHIU�lPgI@1JROQWXBYHIU qu`RG�H ��U =?> `RH^khBhS�kYBhU1KV`Nq `ROQWXBY`LlPKV`
D A
destination
source
compressed video requires 5Mb/s
decompressed video requires 50Mb/s
numbers represent available capacity
de- comp
de- comp
de- comp de-
comp
50
80 100
100 5
10
60
20
50
30 40
the shortest path lacks capacity on resources
de- comp
processing nodes for decompression
! BhgI@1JLK�t�D A � ��BYS1KNHcWRJXO^U1`3]_KNJ�O^M1M�khBhZNOQWXBYHIU ��BmWXG = O^U1S ��BYS�WXGiJLKNon@1BhJLKNApKNU?WX`
WXG�K = O^U1S ��BYS�WXG<JRKVon@1BhJLKNApKNU?W'O^U1S�WXG�KNJRK[]_HIJRK�BY`uO%e^OQkhBhS�ZNHIU�l1gI@1JXObWXBhH^U D'&;B��^K���Bh`RKQqQM�JRH ZNKN`L`RBYU1g
U1H S1KN`�ACO > O^kY`RH = K<JLKNon@1BYJRKNSiWXH GPO e^K OcZNKVJLWXO^BhUiO^ApHI@1U?W�H^] M1JLH�ZVKN`R`LBhU1gpZ OQMPO^ZNBmW > BYU H^JRS1KVJ
WXH GPOQU1S1khK�WRG1K�W O^JLgIKVW�M1JLH�ZVKN`L`RBhU�g1q ��G1BhkYK�`RH^ACK�U1H S1KN`�khO^Z�� WXG�K<JLKNon@1BYJRKNS Z OQMPO^ZNBmW > D
��U HIJRS1KVJ WRHEgI@PO^JRO^U?WXKVK�JRKV`RHI@�JRZNK�O eQO^BYkjO = BhkhBmW > qbWXG1K�O eQO^BYkjO = khK�Z O^M1O^ZNBmW > AE@1`LW = K�ZNHIU �
`RBYS1KNJLKNS q O^` � KNkYk�O^`EWRG1K\ZNHI`3W H^]�K O^Z G/JRKV`RHI@�JRZNKQDf��U"WXG1K\`LKN`L`RBhH^U/ZVHIU�lPg^@1JXOQWRBhHIU"M�JRH = kYKNA
gIBmeIKNU BhU )�JRH = kYKNA r D r�D A q'G1H���K[eIKVJNq � K S1BYS U�H^W<BhU1ZVkh@1S1K ZNO^MPO^ZVBYW > khBYACBmWX`�BhU WXG1KpU1KVW�� HIJ��gIJRO^M1G q'O^U1S ZNH^U1`RBYS1KNJLKNS KVeIKVJ > JLKN`RH^@1JRZVKCBYU ZVHIU�lPg^@1JRBYU1gi`RKN`L`RBYHIU1`<JRKNgIO^JRS1kYKN`L`<HQ] WRG1KpO eQO^BYk �
O = kYK ZNO^MPO^ZVBYW > D+ 'H�M1JRH e BhS�K�JRKV`RHI@�JRZNKV` ��BYWRGEO^S1KVon@POQWXK�Z O^MPOQZNBYW > q� K%gIKVU1KNJRO^khB��NK�WXG1K%JLKN`LHI@1JRZVK
ZNH^U�lPgI@1JROQWXBYHIUpM1JRH = khKNA qnO^U1SCS1Bh`LZN@1`L`�ApKVWRG1H�S�`�]_H^J$WRG1K�g^KNU1KVJXO^kYB �NKVSCM�JRH = kYKNA BYUpWRG1Bh`$Z GPO^M �
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M1JLH = khKVA ��BYWRG WRG1KdO eQO^BYkjO = khK�ZNO^MPO^ZVBYW > OQW�KNO^Z G-JLKN`RH^@1JRZVK `RMFKNZVBYlPKVS-BYUiWRG1K<U1KVW�� HIJ��igIJRO^M1G D
�G1K<M1JRH = khKVA `LWXOQWXKVACKVU?W�BY`�gIBYe^KNU BhU )�JRH = khKNA t�D A D A D
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�G1BY`�M1JRH = khKNA0K�� WRKNU1S1`$)�JRH = khKVA r�D r�D A ]_@1JLWRG1KNJ =?> O^S1S1BYU1g�WXG1K�Z O^MPOQZNBYW > ZNHIU�`LWXJRO^BhU?W�HQ]*KNO^Z GJRKV`RHI@�JRZNK-BhU WXG1KTU1KVW�� HIJ��/gIJRO^M1G q ��G�BhkhK �^KVKNM1BYU1g WRG1K-H = �LKNZVWRBYe^K-H^]�l1U1S1BhU�g WXG�K-HIM�WRBhACO^k
khH Z ObWXBhH^U O^U�S"JRHI@�WRBhU1g ]_@1U1Z[WXBhH^U1`ND #�H^U1S1BYWRBhHIU�` � t�D t �<O^U1S � t�DED �<`3W OQWRK WXGPObWEWXG1K O e^OQBhkjO = khKZ OQMPO^ZNBmW > `RG1H^@1khS = K�`R@ pZNBYKNU?W�WRHEO^ZVZNHIApApH�SPObWXK%WXG�K�WXHQW O^kPZNO^MPO^ZVBYW > ZNHIU�`R@1ApM�WXBYHIUCOQW�KNO^Z G
D?tJRKV`RHI@�JRZNKQD ,THIJRK�`RMFKNZNBmlPZ OQkhk > q1#�H^U1S1BYWRBhHIU � t�D t �$`3W OQWRKN`�WRGPOQW%WRG1K�O eQO^BhkhO = kYK�ZNO^MPO^ZVBYW > OQW%KNO^Z G
M1JLH�ZVKN`R`LBhU1g U1H S1K A @1`LW = K gIJLK OQWRKNJiWXGPO^U HIJiKNon@PO^k�WXH WXG�K WXHQW O^k�ZNO^MPO^ZVBYW > JRKVon@1BhJLKNS7ObW
WXG�K\U1H�S�K =n> WXG1K\gIBmeIKVU/`LKN`L`RBhH^U D ��BYACBYkjO^JLk > q+#�HIU1S�BYWXBYHIU � t�D D �<`LW ObWXKN`cWRGPOQWEWRG1KiO e^OQBhkjO = khK= O^U�S ��BhS�WRGpOQW�K OQZ GpkYBhU ��AE@�`LW = K�gIJRKNOQWXKVJ+WXGPOQUpH^J9KNon@PO^k�WXH�WXG�K%WXH^WXO^k = OQU1S ��BhS�WXGcJRKVon@1BhJLKNS
OQW�WRG1K�khBhU � =?> WXG�K<`LKN`L`RBhH^U D
��KNZNO^khk�WRGPOQWTO U1K�� eQO^JLBjO = khK GPOQ` = KNKVU7O^S�S1KNS WXH"WXG1K U1K[W���HIJ�� gIJXO^M�G ]_HIJ\KNO^Z G
JRKV`RHI@�JRZNK�WXH�K ��M�JRKN`L`'WRG1K$O e^OQBhkjO = khK Z O^MPOQZNBYW > q � ]_HIJ;O�M1JRH ZNKV`R`LBhU1g�U1H S1K$O^U1S � ]_H^J;O�kYBhU �vDu� KJRK[]_KNJ;WXH�WXG1BY` U�KVW�� HIJ���ApH�S1KVknO^` O�ZNO^MPO^ZVBYW > ��ZVHIU1`LWRJXO^BYU1KNSdU1KVW�� HIJ��FD���BmeIKNU<WXG1K$U1K��"U1KVW�� HIJ��
ApH�S1KVk�O^U1S WXG�KTZNO^MPO^ZVBYW > JLKNon@1BhJLKNApKNU?W q ��K U1H�� JLKNZNH^U1`RBYS1KNJcWXG�KTHIM�WXBhACO^k ZNHIU�l1gI@1JXObWXBhH^U
M1JLH = khKVATq ]_H�ZV@1`RBYU1g HIU @1U1BhZNO^`LW�`LKN`L`RBhH^U1`ND
! BhJR`3W qFZNHIU�lPgI@1JLBhU1g `LKN`L`RBhH^U1`�WXG1OQW�S1HCU1H^W�JRKNon@1BYJRKEBYU?WXKNJLACKVS1BjObWXK�M1JRH ZNKV`R`LBhU1g\ZNO^U = K
S1HIU�K `LBhApM1k >2=?> KNkYBhApBhUPObWXBhU�g WXG�K khBYU �n`\WXGPOQW khO^Z��4WXG1K JRKVon@1BhJLKNS = OQU1S ��BhS�WXG ]_JLHIA WXG�K
U1K[W���HIJ��fgIJRO^M1G O^U1Sfl1U1S1BhU�g WXG1K kYK O^`3WcZNH^`LW MPOQWRG"BhUfWRG1K �LJLKNS1@1ZVKNS � U1K[W���H^J��vDf:�KVZ O^@�`RKWXG�K �3JRKNS�@1ZNKVS �-U1K[W���H^J�� ZNHIU?WXO^BhU1`�H^U1k > kYBhU �n` ��BmWXG KNU1H^@1gIG Z O^MPOQZNBYW > ]_HIJ�WXG1K = O^U�S ��BhS�WRGJRKVon@1BhJLKNApKNU?W q�OQU1S U�H kYBhU � Bh` @1`RKVS4ApHIJRK\WXG1O^U H^U1ZNK � BYU/WRG1KikhK OQ`LWpZNHI`3W M1OQWXG � q � K-ZNO^U
gI@POQJXO^U?WXKVK%WXGPObW9WXG1K�H^M�WXBYA O^knZVHIU�lPgI@�JXOQWRBhHIUcZVHIACM�@�WXKVScBhUEWXG�Bh`9U1K[W���H^J�� ��BYkhk�O^k���O > `�`ROQWXBY`L] >
WXG�K<ZNO^MPO^ZVBYW > JLKNon@1BYJRKNApKNU?WND
��UiWXG1K�HQWXG1KVJ�G1O^U1S q = KNZNO^@1`LK Oc`RBYU1gIkYK�JRKV`RHI@1JLZNK�ACO > = K�@1`LKNS AE@1kmWXBhM�khK�WRBhApKN`%BYUiO
`RKVkhKVZVWXKVS ZVHIU�lPgI@�JXOQWRBhHIU quWRG1KC`RO^ApKp`3WXJROQWXKVg > A O > U�H^WdO^k���O > ` � HIJ���]_HIJ�`LKN`R`LBhHIU�`dWXG1OQW<S1H
JRKVon@1BhJLKEBhU?WXKVJRApKNS1BhOQWXKdM1JRH ZNKV`R`LBhU1g1D���U�K���O^ApM1khKdBh`�g^BYeIKVU�BhU�! BhgI@1JLK t�D r�q ��G1KNJLK O `RKV`R`RBYHIU
v
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1,2
cost, available capacity ( processing ) cost, available bandwidth
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]_JRH^A 6pWXHC8-BY`�WXH = K ZVHIU�lPgI@�JRKNS ��BYWRG HIU�KpM�JRH ZNKN`L`RBYU1g-`3WXKNM D ��KNJRKQq WRG1K `RGPO^S�KNS U�H�S1K BY`
DODWXG�KpH^U1k > M�JRH ZNKN`L`RBYU1gTU�H�S1K ZNO^MPO = kYKcH^]�WRG1K M1JRH ZNKV`R`LBhU1g1q O^U1S K OQZ G JLKN`RH^@1JRZVK Bh`�OQ`R`RH ZNBhOQWXKVS
��BYWRGTW�� H eQO^kh@1KV`NqvWXG1K<lPJR`3W = KNBhU�g BYWR`�ZVHI`LW�O^U1S-WRG1K `LKNZVHIU1S = KNBhU�gCWXG�KcO e^OQBhkjO = khK�ZNO^MPO^ZVBYW > D
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d
1,5 1, 1
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Cost, Capacity
this link is used twice, and therefore must accomodate both uses
the least-cost path for a session from s to d requiring 1 unit capacity (projected from the layered graph)
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khKNO^`LW ��ZVHI`LW MPOQWRG Bh`$M1JLH �LKNZ[WXKNS WRH O<ZNHIU�lPgI@1JROQWXBYHIU BYUpWRG1K�HIJLBhgIBYUPO^k1U�KVW�� HIJ��vq ��G1BYZ G H eIKVJR@1`LKN`
O JLKN`RH^@1JRZVK^D�! BhgI@1JLK t�D t � = ��`LG1H���`�WXG1OQW�WRG1K M1JLH �LKNZ[WXKVS�ZNHIU�l1gI@1JXObWXBhH^U-@1`LKN`�WRG1KEkhBYU � �DC @FO��W���BhZVK^q*ZNHIU1`L@1ApBhU1g rp@1U1BmWX`�H^] = O^U�S ��BhS�WRG q ��G�BhkhK�WXG�KEO eQO^BhkhO = khK = O^U1S ��BYS�WXG�ObW�WXG�K khBYU � BY`
HIU1k > A @�U1BYWND � G1BYkhKpWXG1K\`LKN`R`LBhHIU/Z OQU = K\ZVHIU�lPgI@�JRKNS/HIUfWRG1Bh`EM1OQWXG BY]�BmWcJRKVon@1BhJLKN` � s !PB
DbB@1U1BmWX` H^] = O^U1S ��BhS�WRG q�WRG1KNJLK�Bh` U1HEMFHI`R`LB = kYK�MPOQWRG H^WRG1KNJ ��Bh`RKQq = KNZ OQ@1`RK�WRG1K�WRH^W O^k = O^U�S ��BhS�WRG
JRKVon@1BhJLKNApKNU?W K ��ZVKNKVS1` WXG1K-O e^OQBhkjO = khK = OQU1S ��BhS�WXG4H^]�O^U > M1OQWXG ]_JLHIA 6TWXH 8vD 'H lPU�S2OeQO^khBYS ZNH^U�lPgI@1JROQWXBYHIU qF]_HIJ�K OQZ G JLKN`RH^@1JRZVK O S1KNZVBh`RBYHIU�GPO^`�WRH = KcACO^S1K���G1KVWRG1KNJ�WXH\K ��ZNkh@�S1K
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U1HIJ�BhU �%q BmW�O^S1S1` � WXH �%q `LKVWRWRBhU1g WRG1K WRKNU?W OQWRBYe^KcMPO^JRKVU?W�H^] � WXHZOvq B D KQDYq E � � ����OvquOQU1S`RK[WRWRBhU1g WRG1K-WRKNU?W OQWRBYe^K-S1BY`LW OQU1ZNK HQ] � WRH 8 � O �pM1kY@1`CWRG1K-kYKNU1gQWXG4H^] � O @ � � q%B D K^Dmq 8 � � �]�8 � O �I� d�� ��� :�� � O @ � � D�!PHIJ�KNO^Z G�U1H S1K � WXGPOQW�Bh`�BhU �%q BmW�ZVHIACM1O^JRKV` 8 � � ��WXH 8 � O @ � ��M1kh@�`WXG�KdkYKNU1g^WRG-H^] WXG1K<KNS�gIK � O @ � �[qvOQU1S-Bm]9BYW�lPU�S1`�WRGPOQW18 � � �%BY`�khO^JRg^KNJNqPBmW�@1M*S1OQWXKV` 8 � � ��OQU1SE � � �[D ��]�WRG1Ki`RK[W H^] = HI@1U�SPO^J > eIKVJLWXBYZNKV`CBY`EBhApM1khKVACKVU?WXKNS"@�`RBhU�g O�! B = HIUPO^ZVZNB%G1KNO^M � tIr � q(�B ���n`3WXJXO � `�O^kYgIHIJLBYWXG�A JL@1U1`�BhU � �� � � khHIg � �%WRBhApK^q ��G�KNJRK � Bh`%WRG1KdUn@1A = KVJ�HQ]+U1H S1KV`�BYUWXG�K<g^JXO^M1G qPO^U1S � BY`%WXG1K�Un@1A = KNJ�H^] KNS1g^KN`ND
� G�KNU (�B ���n`LWRJXO � `cO^kYgIHIJRBmWXG1A BY`cO^M1M�khBhKVSfWXH O khO > KNJLKNS gIJXOQM1G q�`RHIApK H^]�WRG1K\MPOQWRG1`
BhUfWRG1K\`RG�HIJLWRKN`LWpMPObWXG"WXJLKNKiA O > ZNHIU?WXO^BhU KNS�gIKN` HIU"S1B � KVJRKVUnW khO > KNJL`cWXGPOQW ZVHIJRJLKN`LM*HIU�S WRH
WXG�K `XOQACKpkhBYU ��HIJ<U1H�S�K BhU WXG1KCHIJRBYgIBhU1O^k9U1K[W���HIJ�� ]_JLHIA ��G1BYZ G WXG1KCkjO > KVJRKVS"U1KVW�� HIJ�� ��O^`
ZNH^U1`LWRJR@1Z[WXKNS q9khKNO^S1BhU�giWRHTH e^KNJ ��@1`RKCH^]%JLKN`LHI@1JRZVKN`VD\ H M1JRK[eIKVUnWdWXG1BY`Nq ��KCACH S1Bm] > WRG1K = O^`RBYZ
M1JLH�ZVKN`R`LBhU1gd`LWRKNMCWRHdBYU1ZNkY@1S1K�O�Z G1KNZ�� ]_HIJ�H eIKNJ ��@1`LKNS JLKN`LHI@1JRZVKN`VD$��UCMPO^J3WXBhZV@1kjOQJNq ��G1KVU\O�U1H�S�K
O �;Bh`�O^S1S�KNS\WXHcWXG�K�WRJRKVK � ��S1KVU1H^WXKV`�WXG1K�kjO > KNJ�BhU ��G�BhZ GiWXG1K�e^KNJLWRK��TO^M�M*KNO^JR` �[q � K<ZVHIU1`LBhS1KVJ
KNS�gIKN` H^] WRG1K�]_H^JRA � O �3@ � � ��O^U1S � O � @�O ���+>��[D9:�KV]_HIJLK�M�JRH ZNKN`L`RBYU1gEO^UCKNS1g^K�H^]*WXG1K�]_HIJRA � O �3@ � � ���G1BYZ G = KVkhHIU�gI`�WXH khO > KNJ �Rq � K�K���O^ApBhU�K�WRG1K�M1OQWXGCBhU WXG1K�WXJRKVK�]_JLHIA 6�WXHrO � O^U1S O^S1SC@1M WXG�KZ OQMPO^ZNBmWXBYKN`+JLKNon@1BYJRKNS =?> O^khk KNS�gIKN`9H^UEWXG1K%M1OQWXG WRGPOQW+ZNHIJLJRKN`LM*H^U1ScWXH�WRG1K%HIJLBhgIBYUPO^k?khBYU � � O @ � �[D��]1WRG1Bh`uWXHQW O^k?ZNO^MPO^ZVBYW > qbM1kY@1`'WRG1K$Z O^MPOQZNBYW > WRGPOQW � HI@1khS = K$@1`LKNS =?> WXG�K KVS1gIK � O �3@ � � �[qbK���ZNKVKNS1`WXG�KEO eQO^BhkhO = khK�ZNO^MPO^ZVBYW > H^]9WRG1K kYBhU �vqPWXG�KNU U1H O^ZVWRBhHIUTBh`�W O �QKNU ��BmWXG-JLKN`LM*KVZVW�WRHCWXG1OQW�KVS1gIKQD
!+BYgI@1JRK�t�D Dp`RG1H���`�O^U-K �1OQACM1kYK�H^]+WRG1Bh`�Z OQ`RK^q ��G1KVJRK<W���HCBhU?WXJRO ��khO > KNJ�KNS�gIKN`�ZNHIJLJRKV`RMFHIU1S1BYU1gWXH WXG�KdkYBhU � � O @ � �%O^JLK�ZNHIU1`LBhS1KVJRKVS BhU\WXG�Kd`LG1HIJLWRKN`3W�MPOQWRGTWRJRKNK<JRH H^WRKNSTOQW�WXG1K<U1H S1K 6ID �G1KBhU?WRJXO ��kjO > KVJ�KVS1gIKEZVHIU1`LBhS1KVJRKNS-BhUTWRG1K `LKNZVHIU1S�kjO > KNJ�Z O^U1U�H^W = K @1`LKNS = KNZNO^@1`RK<WXG1K O e^OQBhkjO = khK
Z OQMPO^ZNBmW > � A @1U1BmW�%GPO^`�O^kYJRK OQS >\= KNKNU-@1`RKVS-BhUiWXG�K<lPJL`LW�kjO > KVJND �G1K S1HQWRWXKVSTkYBhU1KV`�`RG1H��.WXG�KMPO^J3W%H^]uWRG1K�`LG1HIJLWRKN`3W�MPOQWXG ZNHIApM1@�WRKNS =?> WRG1K�HIJLBhgIBYUPO^kv(�B ��� `3WXJRO � `�O^khg^HIJRBmWXG1A q ��G1BhZ G\BY`�U1HQW
@1`LKNS =?> WXG�Bh` G1KN@�JRBh`3WXBYZ ApKVWRG1H S S1@�K WRH WRG1KTBYU1`R@ CZVBhKVUnWCZ OQMPO^ZNBmW > D ��S�gIKN`pH^]�WRG1Ki]_HIJRA
� O �3@FO ���+> �[q ��G1BhZ G O^JRK�BhU?WXKVJ ��kjO > KVJ$KVS1gIKV`Nq1OQJRK�GPO^U1S1kYKNSC`RBhApBhkhO^JRk > O^ZNZVHIJRS1BYU1g�WXH�WXG1K�O e^OQBhkjO = khK
D N
v 0
w 0
w 1
v 1
1 unit
1 unit
Both ( v 0 ,w 0 ) and ( v 1 ,w 1 ) are used on the path from s to d within the shortest path tree,
requiring 2 units in total.
s
d
The shortest path tree rooted at the source s is
shown in thick lines.
available capacity
!+BYgI@1JLK�t�DED � ��G1HIJ3WXKV`LW�MPOQWRG WRJRKNK�BYUTOckhO > KNJLKNS-g^JXO^M1G
Z OQMPO^ZNBmW > H^]1WXG�K�M1JLH�ZVKN`R`LBhU1g�U1H�S�KN`9OQ`R`RH ZNBhOQWXKVS ��BYWRGdWRG1KN`LK%KNS1g^KN`ND � K JRKV]_KVJ WRH�WXG�Bh`+ZNO^MPO^ZVBYW >
Z G1KVZ�� BYU1g M�JRH ZNKNS�@1JRK<O^`�Z OQMPO^ZNBmW > WXJRO^Z��nBhU1g�D
��UcWRG1K � HIJR`3W�Z O^`LK^q?WXG1K�K�� WXJRO�WRBhApK�JLKNon@1BhJLKNS =?> ZNO^MPO^ZVBYW > WXJXOQZ�� BYU1g�Bh` � ��� � � � � � � � �[q��G1KVJRK � O^U1S � O^JLK�WXG�K�U @�A = KVJ9H^]FKNS�gIKN`�O^U�ScU1H�S�KN`�BhUdWXG1K�HIJLBhgIBYUPO^knU1K[W���HIJ��cO^U1S � BY`+WXG�KUn@1A = KNJ�H^]+M1JRH ZNKV`R`RBYU1gp`LWXKVM1`ND$ �G1BY`�ZNO^U = K�`RKVKNU =?> U�H^WXBYU1gcWXGPOQW�WRG1K�Z G1KNZ��nBhU�g M1JLH�ZVKNS1@1JLK
Bh`�BYUne^H �^KVS U1H<ApHIJRK�WXG1O^U � ��� � � �9WXBhApKN`VqnO^U1SpK O^Z GCK���KNZV@�WXBYHIU JLKNon@1BYJRKN`�WXG1OQW ��K�WXJRO e^KNJL`RKOcMPOQWRG ��BmWXGiU1HpACHIJLK�WXG1O^U � � A KVS1gIKV`ND
�G�K�JL@1U1U1BYU1g<WRBhApK�Z O^U = K�BYACM�JRH eIKVS =?> ACO^BhU?W OQBhU1BYU1g�O^UCO^S1S�BYWXBYHIUPO^k eQO^JRBhO = khK�� � O � �]_HIJ9KNO^Z G eIKNJ3WXK � BhUEWRG1K�MPO^J3WXBjOQk WRJRKNK�ZVHIU1`LWRJR@1Z[WXKVSC`LH�] OQJND+��] C �vBh` WXG1K%WRKNU?W OQWRBYe^K�MPO^JRKVU?W�H^]�O ��qB D K^Dmq C ��� E � O � �[qFWXG1KVU�� � O � ��S1KVU1H^WXKV`�WXG1K `R@1A H^]�WXG1K Z O^MPOQZNBYWRBhKV`�JRKVon@1BhJLKNS ]_JRH^A OQkhk'KNS1gIKV`HIU WRG1K�WXJLKNK�MPObWXG ]_JRH^A 6�WXH.O � WXG1OQW�O^JLK�ZNHIM�BhKN`�HQ]uWXG1K�kYBhU � �!C @�O ��BhU WRG1K�HIJLBhgIBYUPO^kvU1KVW�� HIJ��gIJRO^M1G D�� BhApBhkjOQJRk > qIBY]�O �� G>j� E � O � �[q WXG1KVU�� � O � �$BY`$WRG1K�`L@1A H^] WXG�K�Z O^M1O^ZNBmWXBhKV` JLKNon@1BYJRKNSC]_JRHIAO^kYk+KNS�gIKN`�HIU�WXG�K WRJRKVKcMPOQWXG�]_JLHIA 6cWXH]O ��WRGPOQW�ZVHIJRJLKN`RMFHIU1S WXH\WRG1KcM1JRH ZNKV`R`LBhU1g U1H S1K.O-BYUWXG�KCHIJLBhgIBYUPO^k U1KVW�� HIJ�� gIJRO^M1G DC��`LBhU1giWXG�KN`RK O^S1S1BmWXBYHIUPO^k'e^OQJRBjO = khKV`Nq ��KpZ OQU WRKNJRApBhU1OQWXKcWXG�K
Z OQMPO^ZNBmW > WXJXOQZ�� BYU1g `LK O^JLZ G ]_JRHIA OpU1H�S�K[O � = O^Z��\WRH�6 K O^JLk > q*JLKNS1@1ZVBhU1gCWXG1K<WXBhApK�W O �QKNU-]_H^JZ OQMPO^ZNBmW > WXJRO^Z��nBhU1gcWRH � � � ��� �[D
��UiM1JRO^ZVWRBhZVK^q�WRG1K�K�� WRJXOEWXBYACK�JRKNon@1BYJRKVS =?> Z O^MPOQZNBYW > WXJRO^Z��nBhU1gcBY`%AE@1Z Gi`RACO^kYkhKNJ�WXG1O^U
WXG�K � HIJR`3W���Z O^`LKEO^UPOQk > `RBY`�`L@1gIgIKV`LWX`Vq = KNZNO^@1`LKEU1KVW�� HIJ�� `�O^JRK�S1KV`RBhg^U1KNS-WRHCG1O e^KE`RACO^kYk S1BjOQA �
KVWRKNJL`Nq ��G�BhZ G�ApK O^U1`�WXGPObW�WRG1K MPObWXG1`�BYUTWRG1K `LG1HIJLWRKN`3W�MPOQWRGTWXJLKNKEg^KNU1KVJXO^kYk > GPO e^KE] O^J�]_K���KVJ
WXG1O^U � � KNS�gIKN`VD$��] � K�khK[W�� S1KNU�H^WXK�WRG1K�ACO ��BhAE@1A Un@1A = KNJ�HQ] KVS1gIKV`�BhU\OEMPObWXG\]_JRHIA WXG�K
B^sJRH H^W�WRHiO eIKVJLWXK � BhU WRG1Kc`RG�HIJLWRKN`LW�M1OQWXG�WXJLKNKQq WXG1KVU WRG1KcK�� WRJXO WXBYACKdJRKNon@1BYJRKVS =?> ZNO^MPO^ZVBYW >
WXJRO^Z��nBhU1g�BY` � � � � � �[D+��e^KNUpWXG1BY`�JRKN`L@1kYW�H e^KNJ ��`LWXOQWXKV`$WRG1K�WXBhApK%JLKNon@1BhJLKNS =?> Z O^M1O^ZNBmW > WXJRO^Z�� �BhU�g BYU M1JXO^Z[WXBYZNK^Dp��` ��BhkYk = K `RKNKVUfkjObWXKNJVquJR@1U�U1BhU1giWXBYACK ACKNO^`R@1JLKNApKNU?WX`<BhU ApHIJRKcJLK O^kYBh`LWRBhZ
`RBmWX@PObWXBhH^U1`�`LG1H�� WXG1OQW�Z OQMPO^ZNBmW > WRJXO^Z��nBhU�gEW O �QKN`�khKV`R`%WRGPO^U\W���BhZVK�WXG1K�WRBhApK�JLKNon@1BhJLKNS =?> WXG�K
`RBYACM�khKNJ�G1KN@1JLBh`3WXBhZV`ND
#%OQMPO^ZNBmW > WXJRO^Z��nBhU1g/KNU�`R@1JLKN`TWRGPOQWiMPObWXG1`\]_HI@1U�S =?> WXG�K OQkhgIHIJLBYWRG1A S1H U�H^WiH eIKNJ �
@1`LKCOQU > JRKN`LHI@1JLZNKN`VDp��H���K[eIKVJNq'`RBhU�ZNKcWXG1KcM�JRH = kYKNA Bh` ��� ��GPO^JRS q � KCZNO^U1U1H^W�K ��M*KVZVW<BYW�WRH
O^k �%O > `<l1U1SfO\eQO^khBYS�MPOQWXG q K[eIKNU ��G1KNU"OiMPOQWRG K ��Bh`LWR`NDi#�H^U1`RBYS1KNJ�WXG�KCK �1OQACM1kYK `RG1H���UfBYU
!+BYgI@1JRK�t�DPB � O �[D9��] K O^Z G kYBhU � BhU WXG1K�HIJRBYgIBhU1O^k1U1K[W���HIJ��Cg^JXO^M1GCGPO^`$HIU1K�@1U1BYW$H^] Z O^MPOQZNBYW > q�OQU1S
u 2
v 2
w 2
x 2
t
u 0
v 0
w 0
x 0
s
u 1
v 1
w 1
x 1
1
Each link and processing node has 1 unit of available capacity
Cannot proceed to w 2 because the capacity of ( u,w ) has already been used up
� ��� � .� � �����#&5�4��'1( �1� ��&5��� � ���-�%$%��� �?����"
A valid path not chosen by the capacity tracking
1 u 2
v 2
w 2
x 2
t
u 0
v 0
w 0
x 0
s
u 1
v 1
w 1
x 1
�)(������A�4.�� �1�0 �� � " �5$%�4���� ��
!+BYgI@1JLK�t�DPB � :�khH Z��^KVSTM1OQWXG BhUiZ OQMPO^ZNBmW > WXJRO^Z��nBhU1g
WXG�K�`RKN`L`RBYHIUiJRKNon@1BYJRKV`�HIU1K�@1U�BYW�H^]'ZNO^MPO^ZVBYW > HIUiK O^Z GiKNS�gIK�H^];WXG1K�`RKNkYKNZ[WXKNS MPOQWRG q�BmW�Z OQU ] O^Bhk
WXH lPU1S-OpM1OQWXG qvOQ`�`LG1H���U BhUiMPOQJLW � O �%H^] WXG1K�lPgI@�JRK^D$ �G1K = HIkYSiKNS1gIKV`�OQJRK�WXG1K<KNS�gIKN`�WXGPObW
]_HIJLA WXG1K<`RG1H^JLWXKV`LW�MPOQWXG WXJLKNKEObW�WRG1K<WRBhApK�WXG1K<MPOQWRG `RKNO^JRZ G-WRKNJLACBYUPOQWXKV`ND��H^WXK�WXG1OQW�WRG1KNJLK
Bh`�U1H ��O > WRHdK � WXKNU�S WXG1K�WXJLKNK�]_@1JLWRG1KNJVqn`RBhU�ZNK�WXG1K�HIU1k > KNS�gIK�kYK O e BhU1g�e^KNJLWRK�� C B GPOQ` OQkhJRKNO^S >= KNKNUp@1`LKNS BYUEWXG1K�WRHIM kjO > KVJNq O^U1S G1KVU1ZNK�Z O^U�U1H^W = K�@�`RKNS O^g?O^BYU D+��UcWRG1K�H^WXG1KVJ�GPO^U1S qnWRG1KNJLK
Bh`�OcMPObWXGiWXGPOQW�ZVHI@1kYS = K�@1`RKVST]_HIJ%WRG1Bh`�`LKN`L`RBhH^U qFO^`�`RG1H���U BhUiMPO^J3W � = �[D
B A����� ����& ��� � �$� �%� � ��� ��� � �
� KEM*KVJL]_HIJLACKVS O `LKVW�HQ]�`RBhA @1kjOQWRBhHIU�`%]_HIJ�WRG1KE`RKV`R`LBhHIU ZVHIU�lPg^@1JXOQWRBhHIU-M1JRH = khKNA WRH KVeQO^kY@POQWRK
WXG�K�G1KV@1JRBY`LWXBYZ ApKVWRG1H S1`+S1BY`RZV@1`R`LKNS `RH�] O^JND ��U WXG1K `RBYAE@1kjObWXBhH^U1`Nq�� K%ZNHIU�`RBhS�KNJRKVS WXG�K�]_HIkhkYH���BhU1g
]_HI@1J�S�B��*KNJRKVU?W�U�KVW�� HIJ�� WRHIM*H^khHIgIBYKN`VD
� 'HIJR@1` � �G1BY` U1K[W���HIJ��4Bh` = O^`LKNS HIU OfgIJLBhS4H^] M D U1H�S�KN`\BhU ��G1BhZ G KVe^KNJ > U1H S1K�GPO^` O^U
HI@�WRgIHIBYU1g�KNS1g^K WRH KNO^Z G H^]�BYWR`c]_HI@1JcU1KVBhgIG = HIJR`��fU1HIJLWRG q$`RHI@�WRG q%KNO^`LWCO^U1S � KN`LW��fO^khHIU�g
WXG�K-gIJLBhS kYBhU1KV`ND �G1K U�H�S1KV` OQW KNS1g^KN` HQ]�WXG1KT`Ron@PO^JLK gIJRBYS OQkh`RH GPO eIK kYBhU �n` WXGPObW � ��JRO^MO^JLHI@1U1S ��WRH�WXG�K%ZNHIJLJRKV`RMFHIU1S1BYU1g�U1H S1K�OQW WXG1K%H^M1M*H^`RBYWRK�KVS1gIK^q?JLKN`L@1kYWRBhU1g�BYUcO�WXH^JR@1`+WRHIMFHIkhHIg > D!+BYgI@1JRK%t�D M `LG1H���`�WRG1K�U1KVW�� HIJ�� WXHIMFHIkYHIg > D �H S1KV`�WRGPOQW�ZNO^U M*KVJL]_HIJLA M1JLH�ZVKN`R`LBhU1gdO^JLK�`RG1H���UO^`�WXJLBjO^U�gIkhKV`ND
!+BhgI@�JRK�t�D M � 'HIJR@1`�U1K[W���H^J��
� ��O^U1S1HIA � �G1BY` U1K[W���H^J�� Bh`dO-JXO^U�S1HIA JRKVgI@1khO^JdU�KVW�� HIJ�� ��BYWRG M D-U�H�S1KV`Nq9KNO^Z G"GPO e BhU1g\DBhU�ZNBhS�KNU?W KVS1gIKV`ND\� K = @1BYkhS WXG1KCU1KVW�� HIJ�� `3W O^J3WXBYU1g ��BmWXG OTJXOQU1S1HIA S1KVgIJRKVK�� = HI@�U1S1KNS WXJRKVK
WXG1OQW%`LMPO^U1`�O^khk M DdU1H�S�KN`Nq WXG1KVU ��K�K���MPO^U1S WRG1K�U�KVW�� HIJ�� =?> O^S�S1BhU1gdKNS1g^KN`%JRO^U1S1HIApk > @1U?WXBhk
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� KcS1KVWRKNJRApBhU�K���G1BYZ G kYBhU �n`�H^]�WXG1KEWRHIMFHIkhHIg > WXH @1`LKE]_HIJ�KNO^Z G WXJROpZ �PH�� OQU1S�G1H��0AE@1Z G
Z OQMPO^ZNBmW > WXH�O^`L`RBYgIUdWRH�K O^Z GckYBhU �vDu� G1BYkhK�WXG1KVJRK�O^JLK�U1H�K�pZNBYKNU?W�O^kYgIHIJLBYWXG�AC` ]_HIJ S1KVWRKNJLACBYU1BhU1g
WXG�K = KV`LW�WRHIM*H^khHIg > ]_H^J�O^U O^J = BYWRJXO^J > `RKVW�HQ]FWRJXOpZ%ZVHIU1`3WXJXOQBhU?WX`Vq^]_HIJ9ZVKNJLWXO^BhU ZNkjOQ`R`RKV`�H^]vWXJROpZ
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�G1K > O^kY`RHE`LG1H���KVS WRGPOQW�S1K[WXKVJRApBhU1BYU1gdWRG1K�HIM�WRBhACO^kPWXHIMFHIkYHIg > Bh`�OEGPO^JRS\M�JRH = kYKNA6]_HIJ%HQWXG1KVJ
Z OQ`RKN`VD-!PHIJ�WRG1HI`RKCGPO^JLS Z OQ`RKN`Vq$��@�M�W O KVW O^k D M�JRKN`LKNU?WXKVS/O^M1M1JLH���BYA OQWRBhHIU O^kYgIHIJLBYWXG�AC` � r A �WXG1OQW�@�WXBYkhB��NK�kYBhU1KNO^J%M1JLHIgIJXOQACApBhU1gEO^U1S OpJLHI@1U1S�BhU1gEWRKNZ G1U1BYon@1KdM�JRHIMFHI`RKVSTBYU � tOC � D
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K OQJRkhBYKNJVq9O-GPOQJRSfM1JLH = kYKNA q+gIBmeIKNUfO^U"O^J = BYWRJXO^J > `RKVWEH^]�WXJROpZ ZNH^U1`LWRJXO^BYUnWR` � r^s� ��G1BhZ G"ZNO^U
M DZNH^U1`RBY`LW H^] � HIJR`3W���Z O^`LK WXJROpZ kYBhApBYWR` = KVW�� KNKNU OQU > W�� H�`LKVWR`+H^]�U1KVW�� HIJ��<U1H S1KN`VD9!PHIJ3WX@1UPObWXKNk > q
!+BYU1gIKNJLGn@�W�M�JRHIMFHI`RKVS\O ApKVWRG1H�SpWXHdZNHIApM1@�WRK�OdkYH���KVJ = HI@1U1SCHIU WXG�K�ZNH^`LW%HQ];O^U > WRHIMFHIkhHIg > q
gIBmeIKNU/O�`RK[W H^]�ZNHIU1`3WXJRO^BhU?WX` OQU1S/O JLHI@�WRBhU1g�MFHIkhBYZ > � r^s� Df��U"WXG1KiO = `RKNU�ZNK H^]�O^U K�pZNBYKNU?W
O^kYgIHIJRBmWXG1A WRGPOQW�`LHIkYe^KN`%WRG1K�gIKNU�KNJXOQk M1JRH = khKVATqnWXG1BY`%ApKVWXG�H�S\ACO �^KV`�BYW�M*HI`L`RB = khK�WRHEKVeQO^kY@POQWRK
O^U > WXHIMFHIkhH^g > q =?> ZNH^ACM1@�WXBhU�gTkYBhU ��ZNO^MPO^ZVBYWXBYKN`Vq�O^U1Sfon@1BYZ��nk > ZNHIApMPO^JLBhU1giWXG1K ZNHI`3WcH^]�WXG�K
S1KV`RBhg^U WXH WRG1K�kYH � KNJ = H^@1U1S WRHES1KVWRKNJLACBYU1K�G1H�� gIH H�SCBYW Bh`VD���U WXG1BY`�Z GPOQM�WXKVJNq � K�`RG�H � G1H��
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WXJROpZ�M1OQWRWRKNJRUpWXGPObW�S1H KN`$U1H^W�e BhH^kjOQWRK�WRG1KN`LK�ZVHIU1`LWRJXO^BYU?WX`$HIUCWRG1K�WRH^W OQk1WXJXO CZ�KNU?WRKNJRBYU1gEOQU1S
khKNO e�BYU1g K O^Z G khH Z ObWXBhH^U q ��G�BhkhK�M�JRH e BhS1BYU1gcWXG1K�khH�� KN`3W�H e^KNJXOQkhk ZVHI`LWND
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O = kYK D1D A `LG1H���`$WRG1K�khBhU �dZNO^MPO^ZVBYWXBYKN`9WRGPOQW$O^JLK�U1KNKVS1KNSpWXHdO^ZNZVHIACApH SPOQWXK%O^U > WXJROpZMPOQWLWXKVJRU O^kYkhH���KVS =?> WXG�KEZNHIU�`LWXJRO^BhU?WR`ND<!PHIJ�K �1OQACM1kYK^q WRG1KEkYBhU � � #�kYKVe^KNkjOQU1S qu�K����$HIJ�� ��BY`
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O = khK D�D A � ��KN`L@1kYWRBhU1gC#%O^M1O^ZNBmWXBhKV`�OQ] WXKVJ�(�BhApKNU1`LBhHIU�BhU1g&uBYU � #%O^M1O^ZNBmW >
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�G1KiS1K[] O^@1kYWEZNHI`3WCHQ]�O�kYBhU � Bh` WRG1KiM1JRH S1@1Z[W H^]�BYWR` = O^U1S ��BYS�WXG BYU/, = �Q`pO^U1S BmWX`EkYKNU1g^WRGBhU ApBhkhKV`ND � �G1KpS1KV`RBhg^U1KNJ<A O > `LM*KVZNBY] > OiS1B � KVJRKNU?WdZNHI`3W MFKNJ<@1U1BmW = O^U1S ��BYS�WXG ]_HIJ<O kYBhU �vq
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� �
NY s
source
50 Mb/s, 0
0 , 0
NY t
Det s Det t
Cle s Cle t
Ind s Ind t
Phili s Phili t
flow bound
cost of the least-cost path from NY to NY when decompression
is required.
copies of nodes in the network (first column)
copies of nodes in the network
(second column)
sink
25 Mb/s , 0
15 Mb/s ,0
25 Mb/s, 1551
0 , 0
0 , 0
0 , 0
15 Mb/s ,0
10 Mb/s ,0
25 Mb/s , 0
unbounded ,2205
cost of the least-cost path from NY to Detroit
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