A fast algorithm for path 2-packing problem

Abstract

Let G = (VG,EG) be an undirected graph, T = {T 1,...,Tk} be a collection of disjoint subsets of nodes. Nodes in T1 ∪ ... ∪ Tk are called terminals, other nodes are called inner. By a T-path P we mean an undirected path such that P connects terminals from distinct sets in T and all internal nodes of P are inner, We study the problem of finding a maximum cardinality collection P of T-paths such that at most two paths in P pass through any node v VG- Our algorithm is purely combinatorial and achieves the time bound of O(mn 2), where n := |VG|, m :=|EG|. © Springer-Verlag Berlin Heidelberg 2007.