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A 25/17Approximation Algorithm for the Stable Marriage Problem with OneSided Ties
, 2010
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R.: The AI conference paper assignment problem
 In: Proceedings of AAAI Workshop on Preference Handling for Artificial Intelligence
, 2007
"... The Conference Paper Assignment Problem (CPAP) is the problem of assigning reviewers to conference paper submissions in a manner intended to minimize whingeing. It is assumed that papers are reviewed by members of a preset program committee (PC), each of whom has the opportunity to bid on papers ..."
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The Conference Paper Assignment Problem (CPAP) is the problem of assigning reviewers to conference paper submissions in a manner intended to minimize whingeing. It is assumed that papers are reviewed by members of a preset program committee (PC), each of whom has the opportunity to bid on papers prior to the assignment algorithm being run. In this survey, we show that CPAP is in P if the only information given is individual program committee members ’ preferences for individual papers. However, if both preferences and ex
Socially stable matchings
 in the Hospitals / Residents problem. CoRR Technical Report 1303.2041. Available from http://arxiv.org/abs/1303.2041
"... In twosided matching markets, the agents are partitioned into two sets. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their ..."
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In twosided matching markets, the agents are partitioned into two sets. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their assigned matches. In this paper we study a generalization of stable matching motivated by the fact that, in most centralized markets, many agents do not have direct communication with each other. Hence even if some blocking pairs exist, the agents involved in those pairs may not be able to coordinate a deviation. We model communication channels with a bipartite graph between the two sets of agents which we call the social graph, and we study socially stable matchings. A matching is socially stable if there are no blocking pairs that are connected by an edge in the social graph. Socially stable matchings vary in size and so we look for a maximum socially stable matching. We prove that this problem is NPhard and, assuming the unique games conjecture, hard to approximate within a factor of 3 2 − ɛ, for any constant ɛ. Weapproximation algorithm. complement the hardness results with a 3 2 1
On Computing Pareto Stable Assignments
"... Assignment between two parties in a twosided matching market has been one of the central questions studied in economics, due to its extensive applications, focusing on different solution concepts with different objectives. One of the most important and wellstudied ones is that of stability, propos ..."
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Assignment between two parties in a twosided matching market has been one of the central questions studied in economics, due to its extensive applications, focusing on different solution concepts with different objectives. One of the most important and wellstudied ones is that of stability, proposed by Gale and Shapley [8], which captures fairness condition in a model where every individual in the market has a preference of the other side. When the preferences have indifferences (i.e., ties), a stable outcome need not be Pareto efficient, causing a loss in efficiency. The solution concept Pareto stability, which requires both stability and Pareto efficiency, offers a refinement of the solution concept stability in the sense that it captures both fairness and efficiency. We study the algorithmic question of computing a Pareto stable assignment in a manytomany matching market model, where both sides of the market can have multiunit capacities (i.e., demands) and can be matched with multiple partners given the capacity constraints. We provide an algorithm to efficiently construct an assignment that is simultaneously stable and Pareto efficient; our result immediately implies the existence of a Pareto stable assignment for this model.
A Tight Approximation Bound for the Stable Marriage Problem with Restricted Ties
"... The problem of finding a maximum cardinality stable matching in the presence of ties and unacceptable partners, called MAX SMTI, is a wellstudied NPhard problem. The MAX SMTI is NPhard even for highly restricted instances where (i) ties appear only in women’s preference lists and (ii) each tie ap ..."
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The problem of finding a maximum cardinality stable matching in the presence of ties and unacceptable partners, called MAX SMTI, is a wellstudied NPhard problem. The MAX SMTI is NPhard even for highly restricted instances where (i) ties appear only in women’s preference lists and (ii) each tie appears at the end of each woman’s preference list. The current best lower bounds on the approximation ratio for this variant are 1.1052 unless P=NP and 1.25 under the unique games conjecture, while the current best upper bound is 1.4616. In this paper, we improve the upper bound to 1.25, which matches the lower bound under the unique games conjecture. Note that this is the first special case of the MAX SMTI where the tight approximation bound is obtained. The improved ratio is achieved via a new analysis technique, which avoids the complicated casebycase analysis used in earlier studies. As a byproduct of our analysis, we show that the integrality gap of natural IP and LP formulations for this variant is 1.25. We also show that the unrestricted MAX SMTI cannot be approximated with less than 1.5 unless the approximation ratio of a certain special case of the minimum maximal matching problem can be improved.
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"... Noname manuscript No. (will be inserted by the editor) An improved approximation algorithm for the stable marriage problem with onesided ties ..."
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Noname manuscript No. (will be inserted by the editor) An improved approximation algorithm for the stable marriage problem with onesided ties
UK Finding Large Stable Matchings∗
, 2008
"... When ties and incomplete preference lists are permitted in the Stable Marriage and Hospitals/Residents problems, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NPhard, even under very severe restrictions on the ..."
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When ties and incomplete preference lists are permitted in the Stable Marriage and Hospitals/Residents problems, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NPhard, even under very severe restrictions on the number, size and position of ties. In this paper, we present two new heuristics for finding large stable matchings in variants of these problems in which ties are on one side only. We describe an empirical study involving these heuristics and the best existing approximation algorithm in such problem contexts. Our results indicate that one of these new heuristics has the best performance of the three algorithms, when applied to realworld and randomlygenerated data sets. This study, and these particular problem variants, are motivated by important applications in large scale centralized matching schemes. 1
unknown title
, 2008
"... 5approximation algorithm for a hard variant of stable marriage ..."
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