NDLI: Routing in Undirected Graphs with Constant Congestion

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Chuzhoy, Julia
Copyright Year	2016
Abstract	Given an undirected graph $G=(V,E)$, a collection $\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of $k$ pairs of its vertices, called demand pairs, and an integer $c$, the goal in the Edge-Disjoint Paths with Congestion problem is to connect the maximum possible number of demand pairs by paths, so that the maximum load on any edge (called edge congestion) does not exceed $c$. We show an efficient randomized algorithm to route $\Omega(\mathsf{OPT}/{\operatorname{poly}}\log k)$ demand pairs with congestion at most 14, where $\mathsf{OPT}$ is the maximum number of pairs that can be simultaneously routed on edge-disjoint paths. The algorithm in fact routes $\Omega({\mathsf{OPT}_{\mathsf{LP}}}/{\operatorname{poly}}\log k)$ pairs, where ${\mathsf{OPT}_{\mathsf{LP}}}$ is the optimal value of the standard multicommodity flow relaxation for the problem. The best previous efficient algorithm that routed $\Omega(\mathsf{OPT}/{\operatorname{poly}}\log n)$ pairs required congestion ${\operatorname{poly}}(\log \log n)$, and for the setting where the maximum allowed congestion is bounded by a constant $c$, the best previous efficient algorithms could only guarantee the routing of $\Omega(\mathsf{OPT}/n^{1/c})$ pairs. We also introduce a new type of vertex sparsifier that we call an integral flow sparsifier; integral flow sparsifiers approximately preserve both fractional and integral routings. We show an algorithm that constructs such sparsifiers.
Starting Page	1490
Ending Page	1532
Page Count	43
File Format	PDF
ISSN	00975397
DOI	10.1137/130910464
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4 (Special Section on the Forty-Fourth Annual ACM Symposium on Theory of Computing (STOC 2012))
Volume Number	45
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2016-08-30
Access Restriction	Subscribed
Subject Keyword	network routing edge-disjoint paths Approximation algorithms Graph theory approximation algorithms Graph algorithms
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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