Refined Inequalities for Stable Marriage

Authors:
Brian Aldershof;Olivia M. Carducci;David C. Lorenc
Affiliations:
Department of Mathematics, Lafayette College, Easton, PA 18042-1781 USA;Department of Mathematics, Lafayette College, Easton, PA 18042-1781 USA;Department of Mathematics, Lafayette College, Easton, PA 18042-1781 USA
Venue:
Constraints
Year:
1999

Citing 6
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Abstract

We consider two approaches to thestable marriage problem: proposal algorithms and describing thestable matching polytope using linear inequalities. We illuminatethe relationship between the two approaches. Beginning with aset of linear inequalities that describe the stable matchingpolytope, we describe a process of refining the set of linearinequalities by eliminating redundant constraints and pruningthe preference lists to eliminate unattainable assignments. Weshow that it is trivial to use the pruned preference lists tofind the firm-optimal and worker-optimal stable matchings. Wethen describe a new procedure that combines a proposal algorithmand our refining process to find a stable matching that doesnot favor one group over the other. Finally, we apply our refiningprocess to problems in which couples submit preferences overpairs of positions.