An approximation algorithm for the clustered path travelling salesman problem
Algorithmic Applications in Management (AAIM)(2023)
摘要
In this paper, we consider the clustered path travelling salesman problem. In this problem, we are given a complete graph G=(V,E) with an edge weight function w satisfying the triangle inequality. In addition, the vertex set V is partitioned into clusters V_1,… ,V_k and s , t are two given vertices of G with s∈ V_1 and t∈ V_k . The objective of the problem is to find a minimum Hamiltonian path of G from s to t , where all vertices of each cluster are visited consecutively. In this paper, we deal with the case that the start-vertex and the end-vertex of the path on each cluster are both specified, and for it we provide a polynomial-time approximation algorithm.
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关键词
Travelling salesman problem,Stacker crane problem,Path,Cluster
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