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Popular matchings
TLDR
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
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Cycle bases in graphs characterization, algorithms, complexity, and applications
TLDR
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
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Additive spanners and (α, β)-spanners
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 graphExpand
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Rank-maximal matchings
TLDR
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
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On Pairwise Spanners
TLDR
We study pairwise spanners, where we require to approximate the u-v distance only for pairs (u,v) in a given set P \subseteq V x V. Expand
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Popular mixed matchings
TLDR
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
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An Õ(mn) Gomory-Hu tree construction algorithm for unweighted graphs
TLDR
We present a fast algorithm for computing a Gomory-Hu tree or cut tree for an unweighted undirected graph G = (V,E). Expand
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New Pairwise Spanners
TLDR
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
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Improved approximation algorithms for two variants of the stable marriage problem with ties
TLDR
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
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Popular matchings in the stable marriage problem
TLDR
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
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