A Bidirectional Local Search for the Stable Marriage Problem

This paper proposes a bidirectional local search algorithm to find the egalitarian and the sex-equal stable matchings in the stable marriage problem. Our approach simultaneously searches forward from the man-optimal stable matching and backwards from the woman-optimal stable matching until the search frontiers meet. By employing a breakmarriage strategy to find stable neighbor matchings of the current stable matching and moving to the best neighbor matching, the forward local search finds the solutions while moving towards the woman-optimal stable matching and the backward local search finds the solutions while moving towards the man-optimal stable matching. Simulations show that our proposed algorithm is efficient for the stable marriage problem.