In this paper, we give the first polynomial-time algorithms to determine if an instance admits a popular matching, and to find a largest such matching, if one exists, and show that the problem has equivalent time complexity to the maximum-cardinality bipartite matching problem.Expand

Cycles in graphs play an important role in many applications, e.g., analysis of electrical networks, analysis of chemical and biological pathways, periodic scheduling, and graph drawing.Expand

An (α, β)-spanner of an unweighted graph <i>G</i> is a subgraph <i>H</i> that distorts distances in <i>G</i> up to a multiplicative factor of α and an additive term β. It is well known that any graph… Expand

We give an algorithm to compute a rank-maximal matching with running time O(min(n + C,C &sqrt;n)m), where n is the number of applicants and posts and m is the total size of the preference lists.Expand

We study the problem of matching applicants to jobs under one-sided preferences; that is, each applicant ranks a non-empty subset of jobs under an order of preference, possibly involving ties.Expand

We seek a sparse subgraph H of G where \mathsf{dist}_H(u,v) is a pairwise spanner with additive stretch \beta and our goal is to construct such subgraphs that are sparser than all-pairs spanners with the same stretch.Expand

We consider the problem of computing a large stable matching in a bipartite graph $$G = (A\cup B, E)$$G=(A∪B,E) where each vertex ranks its neighbors in an order of preference, perhaps involving ties.Expand

We consider the problem of computing a maximum cardinality popular matching in a bipartite graph G=(A@?B,E) where each vertex ranks its neighbors in a strict order of preference.Expand