A 3-Approximation Algorithm for a Particular Case of the Hamiltonian p-Median Problem
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Given a weighted graph G with n vertices and m edges, and a positive integer p, the Hamiltonian p-median problem consists in finding p cycles of minimum total weight such that each vertex of G is in exactly one cycle. We introduce an O(n^6) 3-approximation algorithm for the particular case in which p ≤⌈n-2⌈n/5⌉/3⌉. An approximation ratio of 2 might be obtained depending on the number of components in the optimal 2-factor of G. We present computational experiments comparing the approximation algorithm to an exact algorithm from the literature. In practice much better ratios are obtained. For large values of p, the exact algorithm is outperformed by our approximation algorithm.
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