Modeling Stable Matching Problems with Answer Set Programming

The Stable Marriage Problem (SMP) is a well-known matching problem first introduced and solved by Gale and Shapley (1962). Several variants and extensions to this problem have since been investigated to cover a wider set of applications. Each time a new variant is considered, however, a new algorithm needs to be developed and implemented. As an alternative, in this paper we propose an encoding of the SMP using Answer Set Programming (ASP). Our encoding can easily be extended and adapted to the needs of specific applications. As an illustration we show how stable matchings can be found when individuals may designate unacceptable partners and ties between preferences are allowed. Subsequently, we show how our ASP based encoding naturally allows us to select specific stable matchings which are optimal according to a given criterion. Each time, we can rely on generic and efficient off-the-shelf answer set solvers to find (optimal) stable matchings.Comment: 26 page

Solving stable matching problems using answer set programming

Since the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new algorithm for finding the stable matchings. To address this issue, we propose an encoding of the SMP using answer set programming (ASP), which can straightforwardly be adapted and extended to suit the needs of specific applications. The use of ASP also means that we can take advantage of highly efficient off-the-shelf solvers. To illustrate the flexibility of our approach, we show how our ASP encoding naturally allows us to select optimal stable matchings, i.e. matchings that are optimal according to some user-specified criterion. To the best of our knowledge, our encoding offers the first exact implementation to find sex-equal, minimum regret, egalitarian or maximum cardinality stable matchings for SMP instances in which individuals may designate unacceptable partners and ties between preferences are allowed. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming (TPLP). arXiv admin note: substantial text overlap with arXiv:1302.725

HIV Infection and Sexual Behaviour Among Women With Infertility in Tanzania: A Hospital-Based Study.

Infertility is common in Africa, but virtually no data exist on HIV prevalence among infertile women. Mainly anthropological studies in Africa have shown that infertile women have higher risks of marital instability and possibly also have more sexual partners than fertile women. This study was conducted in a hospital in northwest Tanzania during 1994 and 1995. Women presenting themselves with infertility problems to the outpatient clinic were interviewed, examined and blood was drawn. Women who came to deliver in the hospital, excluding primiparae, were taken as a control group. The analysis was limited to women > or = 24 years. In total 154 infertile and 259 fertile women were included in the study. HIV prevalence was markedly higher among infertile women than among fertile women: 18.2% and 6.6% respectively (adjusted odds ratio [OR] for age, residence and occupation 2.7; 95%-confidence interval [CI]: 1.4-5.3). Data on past sexual behaviour showed that infertile women had more marital breakdowns, more lifetime sexual partners and a higher level of exposure to sexually transmitted diseases (STD). Women with fertility problems appear to have higher HIV prevalence, which justifies more attention for such women in the context of AIDS programmes. In addition, caution is needed when using sentinel surveillance data from antenatal clinics to monitor HIV prevalence

Not truly partnerless: Non-residential partnerships and retreat from marriage in Spain

In Spain, nearly two-thirds of women aged 20-34 have not yet entered their first union. However, almost half of them have a stable partner in a different household. Hence, the drop in marriage rates and low prevalence of cohabitation cannot be rightly interpreted as a decline in partnership formation, but rather as a postponement of co-residential unions. This paper examines the prevalence and determinants of non-residential stable partnerships among young adults (women aged 20-34), in relation to cohabitation and marriage, using a multinomial logit model of current partnership type. The analysis is based on data from the 1999 Spanish Fertility Survey.cohabitation, LAT, partnerships, Spain, union formation

Stable Marriage with Multi-Modal Preferences

We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one "evaluation mode" (e.g., more than one criterion); thus, each agent is equipped with multiple preference lists, each ranking the counterparts in a possibly different way. We introduce and study three natural concepts of stability, investigate their mutual relations and focus on computational complexity aspects with respect to computing stable matchings in these new scenarios. Mostly encountering computational hardness (NP-hardness), we can also spot few islands of tractability and make a surprising connection to the \textsc{Graph Isomorphism} problem

A Measure to Compare Matchings in Marriage Markets

In matching markets the number of blocking pairs is often used as a criterion to compare matchings. We argue that this criterion is lacking an economic interpretation: In many circumstances it will neither reflect the expected extent of partner changes, nor will it capture the satisfaction of the players with the matching. As an alternative, we set up two principles which single out a particularly “disruptive” subcollection of blocking pairs. We propose to take the cardinality of that subset as a measure to compare matchings. This cardinality has an economic interpretation: the subset is a justified objection against the given matching according to a bargaining set characterization of the set of stable matchings. We prove multiple properties relevant for a workable measure of comparison.Stable Marriage Problem, Matching, Blocking Pair, Instability, Matching Comparison, Decentralized Market, Bargaining Set

The outcomes of a couple partnership: the importance of sexuality in the transition from dating to cohabitation, marriage or disruption.

This paper examines new union dynamics in Italy, focusing on non-residential partnerships and studying the various transitions of a couple partnership among more recent cohorts. Data from a national survey conducted in 2006 provide a unique opportunity to examine the dynamics of relationship outcomes considering both an individual and a couple perspective and to verify the relevance of sexuality. In particular, an event history approach was used to study the disruption of a intimate couple relationship or its transition to a cohabitation or a marriage. Results of piecewise constant exponential models for competing risks showed that besides attitudinal factors (associated with socio-demographic background), also some aspects connected with sexuality may be important in affecting the decision whether to marry or cohabit or to end a relationship. In particular, both sexual attitudes of individual and sexual characteristics of the relationship have some effects in the outcome of a couple partnership