A fast algorithm for path 2-packing problem

Let G = (V-G, E-G) be an undirected graph, T = {T-1,..., T-k} be a collection of disjoint subsets of nodes. Nodes in T-1 U... U T-k 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 E VG. Our algorithm is purely combinatorial and achieves the time bound of O(mn(2)), where n:= vertical bar V-G vertical bar, m := vertical bar EG vertical bar.