Technical Report CS0613

TR#:CS0613
Class:CS
Title: GENERAL VERTEX DISJOINT PATHS IN SERIES-PARALLEL GRAPHS
Authors: E. Korach and A. Tal
PDFCS0613.pdf
Abstract: Let G=(V,E) be an undirected graph and let (Si ,Ii) l~~ be k pairs of vertices in G. The vertex disjoint paths problem is to find k paths Ph' .. ,Pt such that Pj connects Sj and tj and any two of these paths may intersect only at a common end point. This problem is NP-complete even for planar graphs. Robenson and Seymour proved that when k is a fIXed integer this problem becomes polynomial. We present a linear time algorithm for solving the decision version of the general problem when the input graph is a series-parallel graph. We show how to modify our method such that the algorithm will solve the constructive version, i.e. it will fmd the solution if such exists. Based on the algorithm we construct a cut condition theorem for the existence of a solution to the problem on series parallel graphs.
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