Related papers: Rank Maximal Matchings -- Structure and Algorithms
We consider the problem of matching applicants to posts where applicants have preferences over posts. Thus the input to our problem is a bipartite graph G = (A U P,E), where A denotes a set of applicants, P is a set of posts, and there are…
We consider manipulation strategies for the rank-maximal matching problem. In the rank-maximal matching problem we are given a bipartite graph $G = (A \cup P, E)$ such that $A$ denotes a set of applicants and $P$ a set of posts. Each…
Given a bipartite graph, where the two sets of vertices are applicants and posts and ranks on the edges represent preferences of applicants over posts, a {\em rank-maximal} matching is one in which the maximum number of applicants is…
In this paper, we consider the problem of computing an optimal matching in a bipartite graph where elements of one side of the bipartition specify preferences over the other side, and one or both sides can have capacities and…
We consider the cheating strategies for the popular matchings problem. The popular matchings problem can be defined as follows: Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P denotes a set of posts and the edges…
Let $G = (A \cup B,E)$ be a bipartite graph where the set $A$ consists of agents or main players and the set $B$ consists of jobs or secondary players. Every vertex has a strict ranking of its neighbors. A matching $M$ is popular if for any…
Let $G$ be a bipartite graph where every node has a strict ranking of its neighbors. For every node, its preferences over neighbors extend naturally to preferences over matchings. Matching $N$ is more popular than matching $M$ if the number…
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.,…
A maximum priority matching is a matching in an undirected graph that maximizes a priority score defined with respect to given vertex priorities. An earlier paper showed how to find maximum priority matchings in unweighted graphs. This…
We study the maximal rank in affine subspaces of symmetric or alternating matrices, in terms of the matching numbers of certain associated graphs. Applications include simple proofs of upper bounds on the dimension of such subspaces in…
We consider the max-size popular matching problem in a roommates instance G = (V,E) with strict preference lists. A matching M is popular if there is no matching M' in G such that the vertices that prefer M' to M outnumber those that prefer…
Here we prove that counting maximum matchings in planar, bipartite graphs is #P-complete. This is somewhat surprising in the light that the number of perfect matchings in planar graphs can be computed in polynomial time. We also prove that…
A $k$-ranking is a vertex $k$-coloring such that if two vertices have the same color any path connecting them contains a vertex of larger color. The rank number of a graph is smallest $k$ such that $G$ has a $k$-ranking. For certain graphs…
Let $G=(U \cup V, E)$ be a bipartite graph, where $U$ represents jobs and $V$ represents machines. We study a new variant of the bipartite matching problem in which each job in $U$ can be matched to at most one machine in $V$, and the…
Based on the success of recommender systems in e-commerce, there is growing interest in their use in matching markets (e.g., labor). While this holds potential for improving market fluidity and fairness, we show in this paper that naively…
We consider popular matching problems in both bipartite and non-bipartite graphs with strict preference lists. It is known that every stable matching is a min-size popular matching. A subclass of max-size popular matchings called dominant…
We study the problem of assigning jobs to applicants. Each applicant has a weight and provides a preference list ranking a subset of the jobs. A matching M is popular if there is no other matching M' such that the weight of the applicants…
Given an assignment of weights w to the edges of a graph G, a matching M in G is called strongly w-maximal if for any matching N the sum of weights of the edges in N\M is at most the sum of weights of the edges in M\N. We prove that if w…
The optimized assignment of staff is of great significance for improving the production efficiency of the society. For specific tasks, the key to optimizing staffing is personnel scheduling. The assignment problem is classical in the…
Popularity is an approach in mechanism design to find fair structures in a graph, based on the votes of the nodes. Popular matchings are the relaxation of stable matchings: given a graph G=(V,E) with strict preferences on the neighbors of…