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Author Chuzhoy, Julia ♦ Li, Shi
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2016
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Approximation algorithms ♦ Edge-disjoint paths ♦ Routing problems
Abstract In the Edge-Disjoint Paths with Congestion problem (EDPwC), we are given an undirected $\textit{n}-vertex$ graph $\textit{G},$ a collection $\textit{M}={$ $(s_{1},t_{1}),&ldots;$ $,(s_{k},t_{k})$ } of pairs of vertices called demand pairs, and an integer $\textit{c}.$ The goal is to connect the maximum possible number of the demand pairs by paths, so that the maximum edge congestion - the number of paths sharing any edge - is bounded by $\textit{c}.$ When the maximum allowed congestion is $\textit{c}$ = 1, this is the classical Edge-Disjoint Paths problem (EDP). The best current approximation algorithm for EDP achieves an $\textit{O}(&sqrt;$ $\textit{n})-approximation$ by rounding the standard multi-commodity flow relaxation of the problem. This matches the Ω (&sqrt; $\textit{n})$ lower bound on the integrality gap of this relaxation. We show an $\textit{O}(poly$ log $\textit{k})-approximation$ algorithm for EDPwC with congestion $\textit{c}$ = 2 by rounding the same multi-commodity flow relaxation. This gives the best possible congestion for a sub-polynomial approximation of EDPwC via this relaxation. Our results are also close to optimal in terms of the number of pairs routed, since EDPwC is known to be hard to approximate to within a factor of ˜ Ω ((log $n)^{1/(c+1)})$ for any constant congestion $\textit{c}.$ Prior to our work, the best approximation factor for EDPwC with congestion 2 was $Õ(n^{3/7}),$ and the best algorithm achieving a polylogarithmic approximation required congestion 14.
Description Author Affiliation: Toyota Technological Institute at Chicago, Chicago, IL (Chuzhoy, Julia); Toyota Technological Institute at Chicago (Li, Shi)
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2016-11-08
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 63
Issue Number 5
Page Count 51
Starting Page 1
Ending Page 51

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Source: ACM Digital Library