
Maximum Matchings and Popularity
Let G be a bipartite graph where every node has a strict ranking of its ...
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Dichotomy Results for Classified RankMaximal Matchings and Popular Matchings
In this paper, we consider the problem of computing an optimal matching ...
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CoreStable Committees under Restricted Domains
We study the setting of committee elections, where a group of individual...
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Polynomially tractable cases in the popular roommates problem
The input of the popular roommates problem consists of a graph G = (V, E...
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ThreeDimensional Popular Matching with Cyclic Preferences
Two actively researched problem settings in matchings under preferences ...
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Matchings under Preferences: Strength of Stability and Tradeoffs
We propose two solution concepts for matchings under preferences: robust...
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AUPCR Maximizing Matchings : Towards a Pragmatic Notion of Optimality for OneSided Preference Matchings
We consider the problem of computing a matching in a bipartite graph in ...
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Matchings and Copeland's Method
Given a graph G = (V,E) where every vertex has weak preferences over its neighbors, we consider the problem of computing an optimal matching as per agent preferences. The classical notion of optimality in this setting is stability. However stable matchings, and more generally, popular matchings need not exist when G is nonbipartite. Unlike popular matchings, Copeland winners always exist in any voting instance – we study the complexity of computing a matching that is a Copeland winner and show there is no polynomialtime algorithm for this problem unless 𝖯 = 𝖭𝖯. We introduce a relaxation of both popular matchings and Copeland winners called semiCopeland winners. These are matchings with Copeland score at least μ/2, where μ is the total number of matchings in G; the maximum possible Copeland score is (μ1/2). We show a fully polynomialtime randomized approximation scheme to compute a matching with Copeland score at least μ/2·(1ε) for any ε > 0.
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