Polynomial-Space Exact Algorithms for the Bipartite Traveling Salesman Problem

Mohd SHAHRIZAN OTHMAN; Aleksandar SHURBEVSKI; Hiroshi NAGAMOCHI

doi:10.1587/transinf.2017FCL0003

Special Section on Foundations of Computer Science — Frontiers of Theoretical Computer Science —

Polynomial-Space Exact Algorithms for the Bipartite Traveling Salesman Problem

Mohd SHAHRIZAN OTHMAN, Aleksandar SHURBEVSKI, Hiroshi NAGAMOCHI

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Keywords: bipartite traveling salesman problem, exact algorithms, polynomial space, divide-and-conquer, Stirling's formula

JOURNAL FREE ACCESS

2018 Volume E101.D Issue 3 Pages 611-612

DOI https://doi.org/10.1587/transinf.2017FCL0003

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Abstract

Given an edge-weighted bipartite digraph G=(A,B;E), the Bipartite Traveling Salesman Problem (BTSP) asks to find the minimum cost of a Hamiltonian cycle of G, or determine that none exists. When |A|=|B|=n, the BTSP can be solved using polynomial space in O^*(4²ⁿn^{log n}) time by using the divide-and-conquer algorithm of Gurevich and Shelah (SIAM Journal of Computation, 16(3), pp.486-502, 1987). We adapt their algorithm for the bipartite case, and show an improved time bound of O^*(4²ⁿ), saving the n^{log n} factor.

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