A Parallel Iterative Improvement Stable Matching Algorithm

Lu, Enyue; Zheng, S. Q.

doi:10.1007/978-3-540-24596-4_7

Cited by 9 publications

(8 citation statements)

References 17 publications

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“…Theorem 1 gives theoretical support to the findings in Quinn [29]. Theorem 1 also addresses the concern expressed in the conclusions of Lu and Zheng [23] where it is claimed that "Most of existing parallel stable matching algorithms cannot guarantee a matching with a small number of unstable pairs within a given time interval." Theorem 1 suggests that if the number of acceptable partners for each participant is bounded, the Gale-Shapley algorithm guarantees a small relative number of unstable edges.…”

Section: Distributed Stable Matchingsupporting

confidence: 60%

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Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

et al. 2009

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We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose-accept rounds executed by the Gale-Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds.We apply our results to give a distributed (2 + )-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating the size of a stable matching.

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Section: Distributed Stable Matchingsupporting

confidence: 60%

“…Quinn [29] observes experimentally that a matching with only a fraction of unstable edges emerges long before the Gale-Shapley algorithm converges. Lu and Zheng [23] propose a parallel algorithm that outperforms the Gale-Shapley algorithm in practice. Theorem 1 gives theoretical support to the findings in Quinn [29].…”

Section: Distributed Stable Matchingmentioning

confidence: 99%

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

et al. 2009

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“…We focus on the model introduced by Immorlica and Mahdian [IM05], in which the the women can have arbitrary preferences over the men, and the men have preference lists of length k over the women, sampled uniformly at random. Our main result is a local computation algorithm which matches all but an arbitrarily small fraction of the participants (this is often called an almost stable matching; see, e.g., [TL84,LZ03]). Furthermore, limited to the matched participants, the matching is stable.…”

Section: Introductionmentioning

confidence: 99%

Local Computation Mechanism Design

HassidimAvinatan

MansourYishay

VardiShai

2016

ACM Trans. Econ. Comput.

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We introduce the notion of local computation mechanism design -designing game theoretic mechanisms that run in polylogarithmic time and space. Local computation mechanisms reply to each query in polylogarithmic time and space, and the replies to different queries are consistent with the same global feasible solution. When the mechanism employs payments, the computation of the payments is also done in polylogarithmic time and space. Furthermore, the mechanism needs to maintain incentive compatibility with respect to the allocation and payments.We present local computation mechanisms for a variety of classical game-theoretical problems: (1) stable matching, (2) job scheduling, (3) combinatorial auctions for unit-demand and k-minded bidders, and (4) the housing allocation problem.For stable matching, some of our techniques may have implications to the global (non-LCA) setting. Specifically, we show that when the men's preference lists are bounded, we can achieve an arbitrarily good approximation to the stable matching within a fixed number of iterations of the Gale-Shapley algorithm.

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“…At this point each seed forms a cluster with all vertices on its waitlist, subject to size constraint (we guarantee that no cluster can be larger than total vertex weight over the number of parts). The fact that we use a classical problem as a subproblem in our heuristic allows us to potentially leverage the previous work in optimizing and parallelizing stable assignment, such as [34], [35] and [22]. The pseudocode is presented in Listing 3.…”

Section: Aggregationmentioning

confidence: 99%

Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning

Shaydulin¹,

Chen²,

Safro³

2019

Multiscale Model. Simul.

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Algorithms for many hypergraph problems, including partitioning, utilize multilevel frameworks to achieve a good trade-off between the performance and the quality of results. In this paper we introduce two novel aggregative coarsening schemes and incorporate them within state-of-the-art hypergraph partitioner Zoltan. Our coarsening schemes are inspired by the algebraic multigrid and stable matching approaches. We demonstrate the effectiveness of the developed schemes as a part of multilevel hypergraph partitioning framework on a wide range of problems.

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A Parallel Iterative Improvement Stable Matching Algorithm

Cited by 9 publications

References 17 publications

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

Local Computation Mechanism Design

Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning

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