Related papers: Stable matching: an integer programming approach
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…
While the existence of a stable matching for the stable roommates problem possibly with incomplete preference lists (SRI) can be decided in polynomial time, SRI problems with some fairness criteria are intractable. Egalitarian SRI that…
For a two-sided ($n$ men/$n$ women) stable matching problem) Gale and Shapley studied a proposal algorithm (men propose/women select, or the other way around), that determines a matching, not blocked by any unmatched pair. Irving used this…
We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to…
We consider a matching problem in a bipartite graph $G$ where every vertex has a capacity and a strict preference order on its neighbors. Furthermore, there is a cost function on the edge set. We assume $G$ admits a perfect matching, i.e.,…
Colloquially, there are two groups, $n$ men and $n$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching.…
Stable marriage of a two-sided market with unit demand is a classic problem that arises in many real-world scenarios. In addition, a unique stable marriage in this market simplifies a host of downstream desiderata. In this paper, we explore…
We study the competition for partners in two-sided matching markets with heterogeneous agent preferences, with a focus on how the equilibrium outcomes depend on the connectivity in the market. We model random partially connected markets,…
We study dynamic decentralized two-sided matching in which players may encounter unanticipated experiences. As they become aware of these experiences, they may change their preferences over players on the other side of the market.…
We study the stable marriage problem in the partial information setting where the agents, although they have an underlying true strict linear order, are allowed to specify partial orders. Specifically, we focus on the case where the agents…
I study a two-sided marriage market in which agents have incomplete preferences -- i.e., they find some alternatives incomparable. The strong (weak) core consists of matchings wherein no coalition wants to form a new match between…
To guarantee all agents are matched in general, the classic Deferred Acceptance algorithm needs complete preference lists. In practice, preference lists are short, yet stable matching still works well. This raises two questions: $\bullet$…
In two-sided matching markets with contracts, quantile (or generalized median) stable mechanisms represent an interesting class that produces stable allocations which can be viewed as compromises between both sides of the market. These…
Nowadays, reaching a high level of employee satisfaction in efficient schedules is an important and difficult task faced by companies. We tackle a new variant of the personnel scheduling problem under unknown demand by considering employee…
In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and…
Score matching is a recently developed parameter learning method that is particularly effective to complicated high dimensional density models with intractable partition functions. In this paper, we study two issues that have not been…
We consider a stochastic matching model with a general compatibility graph, as introduced in \cite{MaiMoy16}. We prove that most common matching policies (including FCFM, priorities and random) satisfy a particular sub-additive property,…
Matching market models ignore prior commitments. Yet many job seekers, for example, are already employed, and the same holds for many other matching markets. I analyze two-sided matching markets with pre-existing binding agreements between…
We prove the existence of explicit linear multistep methods of any order with positive coefficients. Our approach is based on formulating a linear programming problem and establishing infeasibility of the dual problem. This yields a number…
We study stable matching problems where agents have multilayer preferences: There are $\ell$ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC '18] studied such problems with strict preferences,…