A Fast Algorithm for the Path 2-Packing Problem

Let G be an undirected graph and T = {T-1,..., T-k} be a collection of disjoint subsets of nodes. Nodes in T-1 boolean OR ... boolean OR T-k are called terminals, other nodes are called inner. By a T-path we mean a path P 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. Our algorithm is purely combinatorial and has the time complexity O(mn(2)), where n and m denote the numbers of nodes and edges in G, respectively.