Specialised constraints for stable matching problems

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Abstract

The stable marriage problem (SM) and the Hospital / Residents problem (HR) are both stable matching problems. They consist of two sets of objects that need to be matched to each other; in SM men to women, and in HR residents to hospitals. Each set of objects expresses a ranked preference for the objects in the other set, in the form of a preference list. The problem is then to find a matching of one set to the other such that the matching is stable. A matching is stable iff it contains no blocking pairs. A blocking pair in a matching M consists of two objects x and y one from each set(x = man and y = woman for SM or x = hospital and y = resident in HR), such that x and y are not matched in M and both x and y would rather be matched to each other than to there assignment in M. Algorithms have been published for both of these problems and optimal constraint models have been published for the stable marriage problem. So the main question would be why the need for specialised constraint for these problems? The SM algorithm and the optimal constraint encodings all have a time complexity of O(n2), but in practice it can take over a minute for the constraint models to find a solution to a problem of size 45 while the SM algorithm can find a solution in less than two hundredths of a second. There have not been any optimal HR constraint models published, but I assume the same performance gap would exist. The advantage of the constraint solutions are their versatility. Many harder valiants of the stable matching problems can be solved by adding simple side constraints to the existing; models, this is not possible with the matching algorithms. So the motivation behind a specialised constraint is to try and combine the efficiency of the algorithm with the versatility of the constraint models. In the full version of this paper I discuss issues concerning the creation of specialised constraints to solve these problems. I then go on to present some empirical results that suggest that specialised constraints significantly out perform other constraint encodings, in both time and space requirements. © Springer-Verlag Berlin Heidelberg 2005.

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APA

Unsworth, C., & Presser, P. (2005). Specialised constraints for stable matching problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3709 LNCS, p. 869). https://doi.org/10.1007/11564751_107

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