https://hal-u-picardie.archives-ouvertes.fr/hal-03617899Giannakos, A.A.GiannakosHifi, MhandMhandHifiEPROAD - Eco-Procédés Optimisation et Aide à la Décision - UR UPJV 4669 - UPJV - Université de Picardie Jules VerneKheffache, R.R.KheffacheOuafi, RachidRachidOuafiEPROAD - Eco-Procédés Optimisation et Aide à la Décision - UR UPJV 4669 - UPJV - Université de Picardie Jules VerneAn approximation algorithm for the k-fixed depots problemHAL CCSD2017[INFO] Computer Science [cs]DESSAIVRE, Louise2022-03-23 18:08:162022-09-17 17:34:452022-03-23 18:08:16enJournal articles10.1016/j.cie.2017.06.0221In this paper, we consider the k-Depots Hamiltonian Path Problem (k-DHPP) of searching k paths in a graph G, starting from k fixed vertices and spanning all the vertices of G. We propose an approximation algorithm for solving the k-DHPP, where the underlying graph is cubic and 2-vertex-connected. Then, we prove the existence of a 5/3-approximation algorithm that gives a solution with total cost at most (5/3n - 4k-2/3). In this case, the proposed method is based upon searching for a perfect matching, constructing an Eulerian graph and finally a k paths solution, following the process of removing/adding edges. We also present an approximation algorithm for finding a shortest tour passing through all vertices in a factor-critical and 2-vertex connected graph. The proposed algorithm achieves a 7/6-approximation ratio where the principle of the method is based on decomposing the graph into a series of ears. (C) 2017 Published by Elsevier Ltd.