Unsplittable flow in paths and trees and column-restricted packing integer programs

Chandra Chekuri, Alina Ene, Nitish Korula

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

Abstract

We consider the unsplittable flow problem (UFP) and the closely related column-restricted packing integer programs (CPIPs). In UFP we are given an edge-capacitated graph G = (V,E) and k request pairs R1, ..., R k, where each Ri consists of a source-destination pair (si, ti), a demand di and a weight w i. The goal is to find a maximum weight subset of requests that can be routed unsplittably in G. Most previous work on UFP has focused on the no-bottleneck case in which the maximum demand of the requests is at most the smallest edge capacity. Inspired by the recent work of Bansal et al. [3] on UFP on a path without the above assumption, we consider UFP on paths as well as trees. We give a simple O(logn) approximation for UFP on trees when all weights are identical; this yields an O(log2 n) approximation for the weighted case. These are the first non-trivial approximations for UFP on trees. We develop an LP relaxation for UFP on paths that has an integrality gap of O(log2 n); previously there was no relaxation with o(n) gap. We also consider UFP in general graphs and CPIPs without the no-bottleneck assumption and obtain new and useful results.

Original languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 12th International Workshop, APPROX 2009 and 13th International Workshop, RANDOM 2009, Proceedings
Pages42-55
Number of pages14
DOIs
StatePublished - Nov 6 2009
Event12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009 - Berkeley, CA, United States
Duration: Aug 21 2009Aug 23 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5687 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009
CountryUnited States
CityBerkeley, CA
Period8/21/098/23/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Unsplittable flow in paths and trees and column-restricted packing integer programs'. Together they form a unique fingerprint.

Cite this