A shortlist-based bidirectional local search for the stable marriage problem

ABSTRACT This paper proposes a shortlist-based bidirectional local search algorithm to find an approximate solution for either the egalitarian or the sex-equal matching of the stable marriage problem. Our approach simultaneously searches forward from the man-optimal matching and backwards from the woman-optimal matching until the search frontiers meet. By using a shortlist-based breakmarriage strategy to rapidly generate all the stable neighbour matchings of all k-best stable matchings, the forward local search finds the solutions while moving towards the woman-optimal matching and the backward local search finds the solutions while moving towards the man-optimal matching. The experiments demonstrate that our proposed algorithm is efficient for finding an approximate solution to the egalitarian or sex-equal matching of the stable marriage problem.

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