Paper Info
Title
Unsplittable Flow in Paths and Trees and Column-Restricted Packing Integer Programs
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 R 1 , ..., R k , where each R i consists of a source-destination pair (s i ,t i ), a demand d i 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.
Year
DOI
Venue
2009
10.1007/978-3-642-03685-9_4
APPROX-RANDOM
Keywords
Field
DocType
no-bottleneck assumption,integrality gap,simple o,log2 n,column-restricted packing integer programs,weight w i,maximum demand,k request pairs r,lp relaxation,unsplittable flow,maximum weight subset,r k
Integer,Graph,Discrete mathematics,Combinatorics,Flow (psychology),Linear programming relaxation,Mathematics
Conference
Volume
ISSN
Citations 
5687
0302-9743
25
PageRank 
References 
Authors
1.09
36
3
Name
Order
Citations
PageRank
Chandra Chekuri13493293.51
Alina Ene240925.47
Nitish Korula351526.69