Resource Configuration and Network Design in Extensible ...

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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.

Transcript of Resource Configuration and Network Design in Extensible ...

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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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

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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 )

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N��U1S1BhO^UPO^MFHIkYBh`ND H O^ZNZVHIACApH SPOQWXK�OQU > WRJXOpZdWRGPOQW�H = K > `�WRG1KN`LK ZNH^U1`LWRJXO^BYUnWR`NqFWXG1K<U1KVW�� HIJ��

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ZNH^U�lPgI@1JROQWXBYHIU O^khkYH���KVS =?> WRG1K�ZNHIU�`LWXJRO^BhU?WR`�ZNO^U = K�GPO^U�S1khKVS D

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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

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K���MFKNZ[W OQWRBhHIU D

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t d

t d

t d

s

c

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t c

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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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t A

a 2

d 2

c 2

b 2

1

2

1

1

3 2

1

1 1

2

1

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2

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6 4

2

2 2

4 2

2

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t c t c s 0

t d t d

t d t d 1

1

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� 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

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: > 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^]

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s

3

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source

receivers

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3

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2

tree cost = 5

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s

3

2

2

tree cost = 4

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s

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source

3 2 2

receivers

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3 2 2

tree cost = 8

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s

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3 2 2

tree cost = 9

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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

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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

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��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 �

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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 �

WXKVJND

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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

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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

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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

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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

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v

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cost, available capacity ( processing ) cost, available bandwidth

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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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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

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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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� �

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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