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An Implementation of a Combinatorial Approximation Algorithm for Minimum-Cost Multicommodity Flow
[chapter]

1998
*
Lecture Notes in Computer Science
*

*Combinatorial*

*approximation*

*algorithms*in GK95, KP95b, PST95 yield ows with

*costs*slightly larger than the

*minimum*

*cost*and use capacities slightly larger than the given capacities. ... We combine and modify the theoretical ideas in these

*approximation*

*algorithms*to yield

*a*fast, practical

*implementation*solving the minimumcost

*multicommodity*ow problem. ... In this paper we describe MCMCF, our

*implementation*

*of*

*a*

*combinatorial*

*approximation*

*algorithm*

*for*the

*minimum*-

*cost*

*multicommodity*o w problem. ...

##
###
Page 5238 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

, Serge (1-STF-C; Stanford, CA);
Stein, Cliff (1-DTM-C; Hanover, NH)

*An**implementation**of**a**combinatorial**approximation**algorithm**for**minimum*-*cost**multicommodity**flow*. ... We combine and mod- ify the theoretical ideas in these*approximation**algorithms*to yield*a*fast practical*implementation*solving the*minimum**cost*mul- ticommodity*flow*problem. ...##
###
Faster Approximation Algorithms for Generalized Flow

1999
*
ACM-SIAM Symposium on Discrete Algorithms
*

We present faster FPTAS's

dblp:conf/soda/WayneF99
fatcat:d7avppi5o5go7fk37djelnxadq
*for*generalized versions*of*the maximum*flow*,*multicommodity**flow*,*minimum**cost**flow*, and miniium*cost**multicommodity**flow*problems in lossy networks. ...*Combinatorial**approximation*alge rithms*for*generalized*flow*problems. In SODA, 1998. T. Radzik.*Approximate*generalized circulation. CCOP ... Acknowledgments The authors thank &*a*Tardos*for*providing comments on*an*earlier draft and Jeffrey Oldham*for*providing*a*preprint*of*[4] and pointing out the reference [I]. ...##
###
An annotated bibliography of network interior point methods

2003
*
Networks
*

We consider single and

doi:10.1002/net.10087
fatcat:zwiupodkbbhkrmhm34cxpol4cu
*multicommodity*network*flow*problems, as well as preconditioners used in*implementations**of*conjugate gradient methods*for*solving the normal systems*of*equations that arise in interior ... This paper presents*an*annotated bibliography on interior point methods*for*solving network*flow*problems. ...*A*truncated interior point method*for*the solution*of**minimum**cost**flow*problems on*an*undirected*multicommodity*network. ...##
###
Page 5177 of Mathematical Reviews Vol. , Issue 2001G
[page]

2001
*
Mathematical Reviews
*

*For*the

*minimum*-

*cost*

*flow*problem with integral data, the generic version

*of*the cycle-canceling

*algorithm*runs in pseudopolynomial time, but several polynomial-time specific

*implementations*can be ob- ... Summary: “The cycle-canceling

*algorithm*is one

*of*the earliest

*algorithms*to solve the

*minimum*-

*cost*

*flow*problem. ...

##
###
Page 9426 of Mathematical Reviews Vol. , Issue 2001M
[page]

2001
*
Mathematical Reviews
*

The paper proposes

*a*new*approximation**algorithm**for*nonconvex piecewise linear network*flow*problems. ...*For*this case, we*implement**an*iterated version*of*our procedure, based on contracting some arcs*of*the tour produced by*a*first application*of*the*algorithm*, then reapplying the*algorithm*to the shrunken ...##
###
Fast approximation algorithms for multicommodity flow problems

1991
*
Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91
*

Acknowledgments We are grateful to Andrew Goldberg, Tishya Leong, Jim Orlin, Rina Rotshild, David Shimoys and Peter Shor

doi:10.1145/103418.103425
dblp:conf/stoc/LeightonMPSTT91
fatcat:pb2zi5uxeba5bbt4g773hrp4pq
*for*helpful discussions. ... unlimited I ABSTRACT (WUAmUm 200 w@1W In this paper, we describe the first polynomial-time*combinatorial**algorithms**for**approximately*solving the*multicommodity**flow*problem. ... In this paper, we describe the first*combinatorial**approximation**algorithms**for*the concurrent*flow*problem. ...##
###
Network Flows In Optimisation Problems And Their Extensions

2010
*
ECMS 2010 Proceedings edited by A Bargiela S A Ali D Crowley E J H Kerckhoffs
*

Since this network

doi:10.7148/2010-0271-0276
dblp:conf/ecms/Seda10
fatcat:5hmdzdkh65affg4djmqzppkpky
*flow*version belongs to the class*of*NP-hard*combinatorial*problems,*for*large scale instances, it must be solved by*approximation*or heuristic techniques. ... We present*a*stochastic heuristic approach based on*a*simulated annealing*algorithm*. ...*For*some*of*the*flow*problems such as maximum*flow*problem,*minimum**cost**flow*problem, polynomial time*algorithms*are known (Ahuja et al 1993) , others such as integer maximum*multicommodity**flow*problem ...##
###
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities

2000
*
SIAM Journal on Discrete Mathematics
*

Our maximum

doi:10.1137/s0895480199355754
fatcat:cxubrv77xbb6njqeet6sbiuc6q
*multicommodity**flow**algorithm*extends to*an**approximation*scheme*for*the maximum weighted*multicommodity**flow*, which is faster than those implied by previous*algorithms*by*a*factor*of*k/ log ...*For*maximum concurrent*flow*, and*minimum**cost*concurrent*flow*, we present*algorithms*that are faster than the current known*algorithms*when the graph is sparse or the number*of*commodities k is large, ... We thank Cynthia Phillips*for*suggesting*a*simpler presentation*of*the maximum*multicommodity**flow**algorithm*, and Kevin Wayne, Jeffrey Oldham, and*an*anonymous referee*for*helpful comments. ...##
###
Fast and simple approximation schemes for generalized flow

2002
*
Mathematical programming
*

We present fast and simple fully polynomial-time

doi:10.1007/s101070100238
fatcat:7s377km63nhnnm2hvpb7ct2pom
*approximation*schemes (FPTAS)*for*generalized versions*of*maximum*flow*,*multicommodity**flow*,*minimum**cost*maximum*flow*, and*minimum**cost**multicommodity*... This is accomplished in part by introducing*an*efficient method*of*solving*a*sequence*of*generalized shortest path problems. ... We are grateful to Jeffrey*for*providing us with*a*preprint*of*[30] and pointing out the reference [6] . ...##
###
Fast Approximation Algorithms for Multicommodity Flow Problems

1995
*
Journal of computer and system sciences (Print)
*

In this paper, we describe the rst polynomial-time

doi:10.1006/jcss.1995.1020
fatcat:gxw7ucanizeibjvpj5ivkfvhdy
*combinatorial**algorithms**for**approximately*solving the*multicommodity*ow problem. ... In fact, we prove that*a*(simple) k-commodity ow problem can be*approximately*solved by*approximately*solving O(k log 2 n) single-commodity*minimum*-*cost*ow problems. ... Acknowledgments We are grateful to Andrew Goldberg, Tishya Leong, Jim Orlin, Rina Rotshild, David Shmoys and Peter Shor*for*helpful discussions. ...
We present Jetway,

doi:10.1145/2393347.2393388
dblp:conf/mm/FengLL12
fatcat:zo3txo7v2ngynkipvrlis3ytne
*a*new set*of**algorithms*designed to minimize cloud providers' operational*costs*on interdatacenter video traffic, by optimally routing video*flows*in*an*online fashion. ...*Algorithms*in Jetway are designed by following*a*methodical approach based on*an*in-depth theoretical analysis. ...*Algorithm*2 The*combinatorial**minimum*-*cost**multicommodity**flow**algorithm*. ...##
###
Faster Approximation Schemes for Fractional Multicommodity Flow Problems via Dynamic Graph Algorithms
[article]

2010
*
arXiv
*
pre-print

We combine the work

arXiv:1003.5907v2
fatcat:ebzbvz4wfvfsbe4s4jcqowk2hy
*of*Garg and Konemann, and Fleischer with ideas from dynamic graph*algorithms*to obtain faster (1-eps)-*approximation*schemes*for*various versions*of*the*multicommodity**flow*problem. ... some provably optimal terms - the Omega(mn)*flow*-decomposition barrier*for*single-commodity*flow*. ... Acknowledgments We are grateful to Michel Goemans, Debmalya Panigrahi, and anonymous reviewers*for*helpful comments. We also thank Lisa Fleischer, and David Shmoys*for*providing useful references. ...##
###
Faster approximation schemes for fractional multicommodity flow problems via dynamic graph algorithms

2010
*
Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10
*

We combine the work

doi:10.1145/1806689.1806708
dblp:conf/stoc/Madry10
fatcat:zt63k7gnhjelfkhbz43ian2gx4
*of*Garg and Könemann, and Fleischer with ideas from dynamic graph*algorithms*to obtain faster (1 − ε)-*approximation*schemes*for*various versions*of*the*multicommodity**flow*problem. ... provably optimal terms -the Ω(mn)*flow*-decomposition barrier*for*single-commodity*flow*. ... Acknowledgments We are grateful to Michel Goemans, Debmalya Panigrahi, and anonymous reviewers*for*helpful comments. We also thank Lisa Fleischer, and David Shmoys*for*providing useful references. ...##
###
Page 6040 of Mathematical Reviews Vol. , Issue 98I
[page]

1998
*
Mathematical Reviews
*

The author discusses several recent and earlier results in the field

*of**combinatorial*optimization that concern problems on*minimum**cost*multiflows (*multicommodity**flows*) and edge-disjoint paths. ... We examine the struc- ture*of*the problem with two source-destination pairs and provide*an*efficient*implementation**of**a*Dijkstra-like*algorithm*with time complexity @(mn +n? logn). ...
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