Strongly polynomial algorithms for the unsplittable flow problem

Yossi Azar, Oded Regev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We provide the first strongly polynomial algorithms with the best approximation ratio for all three variants of the unsplittable flow problem (UFP). In this problem we are given a (possibly directed) capacitated graph with n vertices and m edges, and a set of terminal pairs each with its own demand and profit. The objective is to connect a subset of the terminal pairs each by a single flow path as to maximize the total profit of the satisfied terminal pairs subject to the capacity constraints. Classical UFP, in which demands must be lower than edge capacities, is known to have an O(√m) approximation algorithm. We provide the same result with a strongly polynomial combinatorial algorithm. The extended UFP case is when some demands might be higher than edge capacities. For that case we both improve the current best approximation ratio and use strongly polynomial algorithms. We also use a lower bound to show that the extended case is provably harder than the classical case. The last variant is the bounded UFP where demands are at most K of the minimum edge capacity. Using strongly polynomial algorithms here as well, we improve the currently best known algorithms. Specifically, for K = 2 our results are better than the lower bound for classical UFP thereby separating the two problems.

Original languageEnglish (US)
Title of host publicationInteger Programming and Combinatorial Optimization - 8th International IPCO Conference, Proceedings
PublisherSpringer Verlag
Pages15-29
Number of pages15
Volume2081
ISBN (Print)3540422250, 9783540422259
StatePublished - 2001
Event8th International Integer Programming and Combinatorial Optimization Conference, IPCO 2001 - Utrecht, Netherlands
Duration: Jun 13 2001Jun 15 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2081
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other8th International Integer Programming and Combinatorial Optimization Conference, IPCO 2001
CountryNetherlands
CityUtrecht
Period6/13/016/15/01

Fingerprint

Strongly Polynomial Algorithm
Polynomials
Profitability
Best Approximation
Profit
Directed graphs
Approximation algorithms
Lower bound
Combinatorial Algorithms
Capacity Constraints
Polynomial Algorithm
Directed Graph
Approximation Algorithms
Maximise
Path
Subset

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Azar, Y., & Regev, O. (2001). Strongly polynomial algorithms for the unsplittable flow problem. In Integer Programming and Combinatorial Optimization - 8th International IPCO Conference, Proceedings (Vol. 2081, pp. 15-29). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2081). Springer Verlag.

Strongly polynomial algorithms for the unsplittable flow problem. / Azar, Yossi; Regev, Oded.

Integer Programming and Combinatorial Optimization - 8th International IPCO Conference, Proceedings. Vol. 2081 Springer Verlag, 2001. p. 15-29 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2081).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Azar, Y & Regev, O 2001, Strongly polynomial algorithms for the unsplittable flow problem. in Integer Programming and Combinatorial Optimization - 8th International IPCO Conference, Proceedings. vol. 2081, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2081, Springer Verlag, pp. 15-29, 8th International Integer Programming and Combinatorial Optimization Conference, IPCO 2001, Utrecht, Netherlands, 6/13/01.
Azar Y, Regev O. Strongly polynomial algorithms for the unsplittable flow problem. In Integer Programming and Combinatorial Optimization - 8th International IPCO Conference, Proceedings. Vol. 2081. Springer Verlag. 2001. p. 15-29. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Azar, Yossi ; Regev, Oded. / Strongly polynomial algorithms for the unsplittable flow problem. Integer Programming and Combinatorial Optimization - 8th International IPCO Conference, Proceedings. Vol. 2081 Springer Verlag, 2001. pp. 15-29 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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