A note on using the resistance-distance matrix to solve Hamiltonian cycle problem
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An instance of Hamiltonian cycle problem can be solved by converting it to an instance of Travelling salesman problem, assigning any choice of weights to edges of the underlying graph. In this note we demonstrate that, for difficult instances, choosing the edge weights to be the resistance distance between its two incident vertices is often a good choice. We also demonstrate that arguably stronger performance arises from using the inverse of the resistance distance. Examples are provided demonstrating benefits gained from these choices.
This work was supported by Australian Research Council Grants LP110100166 and DP150100618. We would also like to thank the anonymous reviewers whose suggestions helped to improve this paper.
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