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 quantitative 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 quantitative preferences, we show that in most cases the desired solutions can be found by adapting existing algorithms for the classical stable marriage problem.
The stable marriage 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. We consider a useful variation of the stable marriage problem, where the men and women express their preferences using a preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these preference lists. In this setting, we study the problem of finding a stable matching that marries as many people as possible. Stability is an …
The stable marriage (SM) 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 formulation, n men and n women express their preferences (via a strict total order) over the members of the other sex. Solving a SM problem means finding a stable marriage where stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. We consider both the classical stable marriag…
Department of Computing Science（计算机科学系）；University of Glasgow（格拉斯哥大学）
We present an n-ary constraint for the stable marriage problem. This constraint acts between two sets of integer variables where the domains of those variables represent preferences. Our constraint enforces stability and disallows bigamy. For a stable marriage instance with $n$ men and $n$ women we require only one of these constraints, and the complexity of enforcing arc-consistency is $O(n^2)$ which is optimal in the size of input. Our computational studies show that our n-ary constraint is significantly faster and more space efficient than the encodings presented in \cite{cp01}. We also int…
In many labor markets, workers and firms are connected via affiliative relationships. A management consulting firm wishes to both accept the best new workers but also place its current affiliated workers at strong firms. Similarly, a research university wishes to hire strong job market candidates while also placing its own candidates at strong peer universities. We model this affiliate matching problem in a generalization of the classic stable marriage setting by permitting firms to state preferences over not just which workers to whom they are matched, but also to which firms their affiliated…
We present a unified logical framework for representing and reasoning about both quantitative and qualitative preferences in fuzzy answer set programming, called fuzzy answer set optimization programs. The proposed framework is vital to allow defining quantitative preferences over the possible outcomes of qualitative preferences. We show the application of fuzzy answer set optimization programs to the course scheduling with fuzzy preferences problem. To the best of our knowledge, this development is the first to consider a logical framework for reasoning about quantitative preferences, in gene…
We present a unified logical framework for representing and reasoning about both probability quantitative and qualitative preferences in probability answer set programming, called probability answer set optimization programs. The proposed framework is vital to allow defining probability quantitative preferences over the possible outcomes of qualitative preferences. We show the application of probability answer set optimization programs to a variant of the well-known nurse restoring problem, called the nurse restoring with probability preferences problem. To the best of our knowledge, this deve…
Sabanci University（萨班哲大学）；University of Glasgow（格拉斯哥大学）
The Stable Roommates problem (SR) is characterized by the preferences of agents over other agents as roommates: each agent ranks all others in strict order of preference. A solution to SR is then a partition of the agents into pairs so that each pair shares a room, and there is no pair of agents that would block this matching (i.e., who prefers the other to their roommate in the matching). There are interesting variations of SR that are motivated by applications (e.g., the preference lists may be incomplete (SRI) and involve ties (SRTI)), and that try to find a more fair solution (e.g., Egalit…
Technische Universität Berlin（柏林工业大学）；AGH University（AGH大学）
Focusing on Stable Roommates (SR) instances, we contribute to the toolbox for conducting experiments for stable matching problems. We introduce a polynomial-time computable pseudometric to measure the similarity of SR instances, analyze its properties, and use it to create a map of SR instances. This map visualizes 460 synthetic SR instances (each sampled from one of ten different statistical cultures) as follows: Each instance is a point in the plane, and two points are close on the map if the corresponding SR instances are similar to each other. Subsequently, we conduct several exemplary exp…
While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this problem, the existing literature on matching with externalities permits agents to provide complete and total rankings over matchings based off of both their own and their affiliates' matches. This complete ordering restriction is unrealistic, and further the model may have an empty core. To address this, we introduce the Dichotomous Affiliate Stable Matching (DA…
Monash University（蒙纳士大学）；University of Naples “Federico II”（那不勒斯费德里科二世大学）；Sapienza University of Rome（罗马大学）；University of Sydney（悉尼大学）；University of Oxford（牛津大学）
The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act independently and strategically in pursuit of personal preferences. In this article, we study these games in the context of finite-memory strategies, and we assume players' preferences are defined by a qualitative and a quantitative objective, which are related by a lexicographic order: a player first prefers to satisfy its qualitative objective (given as a formula o…
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 ind…
University of Padova（帕多瓦大学）；SRI International（SRI国际）
In real-life temporal scenarios, uncertainty and preferences are often essential and coexisting aspects. We present a formalism where quantitative temporal constraints with both preferences and uncertainty can be defined. We show how three classical notions of controllability (that is, strong, weak, and dynamic), which have been developed for uncertain temporal problems, can be generalized to handle preferences as well. After defining this general framework, we focus on problems where preferences follow the fuzzy approach, and with properties that assure tractability. For such problems, we pro…
Department of Computing, Imperial College London, UK（帝国理工学院计算系）；School of Computer Science and Informatics, Cardiff University, UK（卡迪夫大学计算机科学与信息学学院）；Department of Computing Science, Umeå University, Sweden（乌梅大学计算科学系）
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 o…
RetinalGPT: A Retinal Clinical Preference Conversational Assistant Powered by Large Vision-Language Models
School of Computing and Augmented Intelligence, Arizona State University（亚利桑那州立大学计算与增强智能学院）；School of Computing, Clemson University（克莱姆森大学计算机学院）；Washington University School of Medicine in St. Louis（圣路易斯华盛顿大学医学院）；The Keck School of Medicine of the University of Southern California（南加州大学凯克医学院）；Mayo Clinic（梅奥诊所）；Banner Alzheimer’s Institute（班纳阿尔茨海默病研究所）
