TY - GEN

T1 - Unsplittable flow in paths and trees and column-restricted packing integer programs

AU - Chekuri, Chandra

AU - Ene, Alina

AU - Korula, Nitish

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70350614880&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-03685-9_4

DO - 10.1007/978-3-642-03685-9_4

M3 - Conference contribution

AN - SCOPUS:70350614880

SN - 3642036848

SN - 9783642036842

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 42

EP - 55

BT - Approximation, Randomization, and Combinatorial Optimization

T2 - 12th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2009 and 13th International Workshop on Randomization and Computation, RANDOM 2009

Y2 - 21 August 2009 through 23 August 2009

ER -