### A Polylogarithmic Approximation Algorithm for Edge-Disjoint Paths with Congestion 2A Polylogarithmic Approximation Algorithm for Edge-Disjoint Paths with Congestion 2 Access Restriction
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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