A LP-based Approximation Algorithm for generalized Traveling Salesperson Path Problem

Hamiltonian path problem is one of the fundamental problems in graph theory, the aim is to find a path in the graph that visits each vertex exactly once. In this paper, we consider a generalizedized problem: given a complete weighted undirected graph G = (V, E, c), two specified vertices s and t, let V' and E' be subsets of V and E, respectively. We aim to find an s-t path which visits each vertex of V' and each edge of E' exactly once with minimum cost. Based on LP rounding technique, we propose a 9-root 33/2-approximation algorithm.