Three Fast Algorithms for Four Problems in Stable Marriage

Gusfield, Dan

doi:10.1137/0216010

Cited by 157 publications

(197 citation statements)

References 7 publications

Supporting

Mentioning

192

Contrasting

Unclassified

Order By: Relevance

“…each set in a preference list has size at most 2). If there are no ties, the problem of finding an egalitarian or minimum regret stable set is solvable in polynomial time [13,10]. Since all stable sets consist of n couples in the classical SMP, the G-S algorithm trivially finds a maximum (or minimum) cardinality [7].…”

Section: Definitionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling Stable Matching Problems with Answer Set Programming

Clercq

Schockaert

Cock

et al. 2013

Theory, Practice, and Applications of Rules on the Web

View full text Add to dashboard Cite

The Stable Marriage Problem (SMP) is a well-known matching problem first introduced and solved by Gale and Shapley [7]. 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.

show abstract

Section: Definitionmentioning

confidence: 99%

“…[10,13,20]). In this paper, we propose to use Answer Set Programming (ASP) as a general vehicle for modeling a large class of extensions and variations of the SMP.…”

Section: Introductionmentioning

confidence: 99%

Modeling Stable Matching Problems with Answer Set Programming

Clercq

Schockaert

Cock

et al. 2013

Theory, Practice, and Applications of Rules on the Web

View full text Add to dashboard Cite

show abstract

“…Stable marriage problems with weighted preferences have been studied also in (Gusfield, 1987;Irving et al, 1987). However, they solve these problems by looking at the stable marriages that maximize the sum of the weights of the married pairs, where the weights depend on the specific criteria used to find an optimal solution, that can be minimum regret criterion (Gusfield, 1987), the egalitarian criterion (Irving et al, 1987) or the Lex criteria (Irving et al, 1987).…”

Section: Introductionmentioning

confidence: 99%

“…However, they solve these problems by looking at the stable marriages that maximize the sum of the weights of the married pairs, where the weights depend on the specific criteria used to find an optimal solution, that can be minimum regret criterion (Gusfield, 1987), the egalitarian criterion (Irving et al, 1987) or the Lex criteria (Irving et al, 1987). Therefore, they consider as stable the same marriages that are stable when we don't consider the weights.…”

Section: Introductionmentioning

confidence: 99%

Stability in Matching Problems With Weighted Preferences

2011

Proceedings of the 3rd International Conference on Agents and Artificial Intelligence

View full text Add to dashboard Cite

Abstract:The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools or more generally to any two-sided market. In the classical stable marriage problem, both men and women express a strict preference order over the members of the other sex, in a qualitative way. Here we consider stable marriage problems with weighted preferences: each man (resp., woman) provides a score for each woman (resp., man). Such problems are more expressive than the classical stable marriage problems. Moreover, in some real-life situations it is more natural to express scores (to model, for example, profits or costs) rather than a qualitative preference ordering. In this context, we define new notions of stability and optimality, and we provide algorithms to find marriages which are stable and/or optimal according to these notions. While expressivity greatly increases by adopting weighted preferences, we show that in most cases the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem.

show abstract

“…Often it is beneficial to work with a stable matching that is fair to all agents in a precise sense [11,16]. One such fairness concept can be defined as follows.…”

Section: Introductionmentioning

confidence: 99%