An approximation algorithm for the k-fixed depots problem

作者：Giannakos A; Hifi M^*; Kheffache R; Ouafi R

来源：Computers & Industrial Engineering, 2017, 111: 50-55.

DOI：10.1016/j.cie.2017.06.022

• Approximation
• Cubic
• Factor-critical
• k-Depots
• TSP

In 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.

• 出版日期2017-9