Related papers: Deepening the (Parameterized) Complexity Analysis …
The stable roommates problem is a non-bipartite version of the well-known stable matching problem. Teo and Sethuraman proved that, for each instance of the stable roommates problem in a complete graph, there exists a linear inequality…
Stable matching is a fundamental problem studied both in economics and computer science. The task is to find a matching between two sides of agents that have preferences over who they want to be matched with. A matching is stable if no pair…
We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more…
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…
In the Stable Roommates problem, we seek a stable matching of the agents into pairs, in which no two agents have an incentive to deviate from their assignment. It is well known that a stable matching is unlikely to exist, but a stable…
In the roommate matching model, given a set of 2n agents and n rooms, we find an assignment of a pair of agents to a room. Although the roommate matching problem is well studied, the study of the model when agents have preference over both…
In the Shift Bribery problem, we are given an election (based on preference orders), a preferred candidate $p$, and a budget. The goal is to ensure that $p$ wins by shifting $p$ higher in some voters' preference orders. However, each such…
The past few years have seen a surge of work on fairness in allocation problems where items must be fairly divided among agents having individual preferences. In comparison, fairness in settings with preferences on both sides, that is,…
Super-stability is one of the stability concepts in the stable matching problem with ties. It is known that there may not exist a super-stable matching, and the existence of a super-stable matching can be checked in polynomial time. In this…
The classical Hospitals/Residents problem (HR) models the assignment of junior doctors to hospitals based on their preferences over one another. In an instance of this problem, a stable matching M is sought which ensures that no blocking…
In this paper, we study the Hospitals / Residents problem with Couples (HRC), where a solution is a stable matching or a report that none exists. We present a novel polynomial-time algorithm that can find a near-feasible stable matching…
In 1976, Knuth asked if the stable marriage problem (SMP) can be generalized to marriages consisting of 3 genders. In 1988, Alkan showed that the natural generalization of SMP to 3 genders ($3$GSM) need not admit a stable marriage. Three…
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.…
Given $n$ men, $n$ women, and $n$ dogs, each man has an incomplete preference list of women, each woman does an incomplete preference list of dogs, and each dog does an incomplete preference list of men. We understand a family as a triple…
Motivated by the increasing interest in the explicit representation and handling of various "preference" structures arising in modern digital economy, this work introduces a new class of "one-to-many stable-matching" problems where a set of…
Consider the standard hospitals/residents problem, or the two-sided many-to-one stable matching problem, and assume that the true preference lists of both sides are complete and strict. The lists actually submitted, however, are truncated.…
We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances…
We study the problem of finding "fair" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). In particular, we seek stable matchings that are optimal with respect to profile, which is a vector that indicates the…
Stability is crucial in matching markets, yet in many real-world settings - from hospital residency allocations to roommate assignments - full stability is either impossible to achieve or can come at the cost of leaving many agents…
The Hospital Residents problem with sizes (HRS) is a generalization of the well-studied hospital residents (HR) problem. In the HRS problem, an agent $a$ has a size $s(a)$ and the agent occupies $s(a)$ many positions of the hospital $h$…