Related papers: Modifying an Instance of the Super-Stable Matching…
We introduce the {\sc classified stable matching} problem, a problem motivated by academic hiring. Suppose that a number of institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences…
We give a strongly polynomial time algorithm which determines whether or not a bivariate polynomial is real stable. As a corollary, this implies an algorithm for testing whether a given linear transformation on univariate polynomials…
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.…
Two-sided matching markets describe a large class of problems wherein participants from one side of the market must be matched to those from the other side according to their preferences. In many real-world applications (e.g. content…
The Student-Project Allocation problem with lecturer preferences over Students (SPA-S) involves assigning students to projects based on student preferences over projects, lecturer preferences over students, and the maximum number of…
Several countries successfully use centralized matching schemes for school or higher education assignment, or for entry-level labour markets. In this paper we explore the computational aspects of a possible similar scheme for assigning…
Stable matching in a community consisting of men and women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley, who…
Research regarding the stable marriage and roommate problem has a long and distinguished history in mathematics, computer science and economics. Stability in this context is predominantly core stability or one of its variants in which each…
We consider the stable matching problem when the preference lists are not given explicitly but are represented in a succinct way and ask whether the problem becomes computationally easier and investigate other implications. We give…
In this paper we study the complexity of solving a problem when a solution of a similar instance is known. This problem is relevant whenever instances may change from time to time, and known solutions may not remain valid after the change.…
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…
We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of \cite{chambers2017choice} by weakening the path independence assumption. For many-to-many…
An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…
The efficient computation of large matchings with desirable guarantees is a crucial objective in market design. However, even in simple two-sided matching markets with weak ordinal preferences, finding a maximum-size stable matching is…
A pattern p (i.e., a string of variables and terminals) matches a word w, if w can be obtained by uniformly replacing the variables of p by terminal words. The respective matching problem, i.e., deciding whether or not a given pattern…
We consider the three-dimensional stable matching problem with cyclic preferences, a problem originally proposed by Knuth. Despite extensive study of the problem by experts from different areas, the question of whether every instance of…
Stable matching theory is the foundation of centralized clearinghouses worldwide, from school choice programs to medical residency allocations. However, incorporating complex distributional goals-such as multi-dimensional diversity quotas…
We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to…
Recently MV18 identified and initiated work on the new problem of understanding structural relationships between the lattices of solutions of two "nearby" instances of stable matching. They also gave an application of their work to finding…
We study the Popular Matching problem in multiple models, where the preferences of the agents in the instance may change or may be unknown/uncertain. In particular, we study an Uncertainty model, where each agent has a possible set of…