eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-06-22
15:1
15:15
10.4230/LIPIcs.SWAT.2016.15
article
On Routing Disjoint Paths in Bounded Treewidth Graphs
Ene, Alina
Mnich, Matthias
Pilipczuk, Marcin
Risteski, Andrej
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol053-swat2016/LIPIcs.SWAT.2016.15/LIPIcs.SWAT.2016.15.pdf
Algorithms and data structures
disjoint paths
treewidth