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

Andrew V. Goldberg, Jeffrey D. Oldham, Serge Plotkin, Cliff Stein
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.  ... 
doi:10.1007/3-540-69346-7_26 fatcat:3mvi6wpd6fao3liuemwi22i7ze

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

Kevin D. Wayne, Lisa Fleischer
1999 ACM-SIAM Symposium on Discrete Algorithms  
We present faster FPTAS's 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].  ... 
dblp:conf/soda/WayneF99 fatcat:d7avppi5o5go7fk37djelnxadq

An annotated bibliography of network interior point methods

Mauricio G. C. Resende, Geraldo Veiga
2003 Networks  
We consider single and 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.  ... 
doi:10.1002/net.10087 fatcat:zwiupodkbbhkrmhm34cxpol4cu

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

Tom Leighton, Clifford Stein, Fillia Makedon, Éva Tardos, Serge Plotkin, Spyros Tragoudas
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 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.  ... 
doi:10.1145/103418.103425 dblp:conf/stoc/LeightonMPSTT91 fatcat:pb2zi5uxeba5bbt4g773hrp4pq

Network Flows In Optimisation Problems And Their Extensions

Milos Seda
2010 ECMS 2010 Proceedings edited by A Bargiela S A Ali D Crowley E J H Kerckhoffs  
Since this network 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  ... 
doi:10.7148/2010-0271-0276 dblp:conf/ecms/Seda10 fatcat:5hmdzdkh65affg4djmqzppkpky

Approximating Fractional Multicommodity Flow Independent of the Number of Commodities

Lisa K. Fleischer
2000 SIAM Journal on Discrete Mathematics  
Our maximum 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.  ... 
doi:10.1137/s0895480199355754 fatcat:cxubrv77xbb6njqeet6sbiuc6q

Fast and simple approximation schemes for generalized flow

Lisa K. Fleischer, Kevin D. Wayne
2002 Mathematical programming  
We present fast and simple fully polynomial-time 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] .  ... 
doi:10.1007/s101070100238 fatcat:7s377km63nhnnm2hvpb7ct2pom

Fast Approximation Algorithms for Multicommodity Flow Problems

T. Leighton, F. Makedon, S. Plotkin, C. Stein, E. Tardos, S. Tragoudas
1995 Journal of computer and system sciences (Print)  
In this paper, we describe the rst polynomial-time 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.  ... 
doi:10.1006/jcss.1995.1020 fatcat:gxw7ucanizeibjvpj5ivkfvhdy

Jetway

Yuan Feng, Baochun Li, Bo Li
2012 Proceedings of the 20th ACM international conference on Multimedia - MM '12  
We present Jetway, 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.  ... 
doi:10.1145/2393347.2393388 dblp:conf/mm/FengLL12 fatcat:zo3txo7v2ngynkipvrlis3ytne

Faster Approximation Schemes for Fractional Multicommodity Flow Problems via Dynamic Graph Algorithms [article]

Aleksander Madry
2010 arXiv   pre-print
We combine the work 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.  ... 
arXiv:1003.5907v2 fatcat:ebzbvz4wfvfsbe4s4jcqowk2hy

Faster approximation schemes for fractional multicommodity flow problems via dynamic graph algorithms

Aleksander Madry
2010 Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10  
We combine the work 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.  ... 
doi:10.1145/1806689.1806708 dblp:conf/stoc/Madry10 fatcat:zt63k7gnhjelfkhbz43ian2gx4

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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