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oai:drops-oai.dagstuhl.de:6037 2024-03-06T10:37:30Z ddc:004 open_access

On Routing Disjoint Paths in Bounded Treewidth Graphs Ene, Alina Mnich, Matthias Pilipczuk, Marcin Risteski, Andrej Algorithms and data structures disjoint paths treewidth We study the problem of routing on disjoint paths in bounded treewidth graphs with both edge and node capacities. The input consists of a capacitated graph G and a collection of k source-destination pairs M = (s_1, t_1), ..., (s_k, t_k). The goal is to maximize the number of pairs that can be routed subject to the capacities in the graph. A routing of a subset M' of the pairs is a collection P of paths such that, for each pair (s_i, t_i) in M', there is a path in P connecting s_i to t_i. In the Maximum Edge Disjoint Paths (MaxEDP) problem, the graph G has capacities cap(e) on the edges and a routing P is feasible if each edge e is in at most cap(e) of the paths of P. The Maximum Node Disjoint Paths (MaxNDP) problem is the node-capacitated counterpart of MaxEDP. In this paper we obtain an O(r^3) approximation for MaxEDP on graphs of treewidth at most r and a matching approximation for MaxNDP on graphs of pathwidth at most r. Our results build on and significantly improve the work by Chekuri et al. [ICALP 2013] who obtained an O(r * 3^r) approximation for MaxEDP. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Alina Ene and Matthias Mnich and Marcin Pilipczuk and Andrej Risteski 2016 Is Part Of LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SWAT.2016.15 urn:nbn:de:0030-drops-60378 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.15 eng https://creativecommons.org/licenses/by/3.0/legalcode