A 3/2-approximation algorithm for the multiple Hamiltonian path problem with no prefixed endpoints.

We study the multiple Hamiltonian path problem (MHPP) defined on a complete undirected graph G with n vertices. The edge weights of G are non-negative and satisfy the triangle inequality. The MHPP seeks to find a collection of k paths with exactly one visit to each vertex of G with the minimum total edge weight, where endpoints of the paths are not prefixed. We present a 3/2-approximation algorithm for MHPP with time complexity O (n3) for arbitrary k > 1.& COPY; 2023 Elsevier B.V. All rights reserved.