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A Lattice Linear Predicate Parallel Algorithm for the Housing Market Problem

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Stabilization, Safety, and Security of Distributed Systems (SSS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13046))

Abstract

It has been shown that Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this paper, we give an LLP algorithm for the Housing Market problem. The Housing Market problem is a one-sided matching problem with n agents and n houses. Each agent has an initial allocation of a house and a totally ordered preference list of houses. The goal is to find a matching between agents and houses such that no strict subset of agents can improve their outcome by exchanging houses with each other rather than going with the matching. Gale’s celebrated Top Trading Cycle algorithm to find the matching requires \(O(n^2)\) time. Our parallel algorithm has expected time complexity \(O(n \log ^2 n)\) with and expected work complexity of \(O(n^2 \log n)\).

Supported by the NSF Grant CCR-1812351 and Cullen Trust Endowed Professorship.

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Notes

  1. 1.

    The class CC (Comparator Circuits) is the complexity class containing decision problems which can be solved by comparator circuits of polynomial size.

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Acknowledgments

I thank Changyong Hu, Robert Streit, and Xiong Zheng for various discussions on the housing allocation problem. I also thank the anonymous reviewers for comments on the paper.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, 78712, USA

    Vijay K. Garg

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  1. Vijay K. Garg
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Correspondence to Vijay K. Garg .

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Editors and Affiliations

  1. University of Bordeaux, Bordeaux, France

    Colette Johnen

  2. Chalmers University of Technology, Gothenburg, Sweden

    Elad Michael Schiller

  3. University of Vienna, Vienna, Austria

    Stefan Schmid

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Garg, V.K. (2021). A Lattice Linear Predicate Parallel Algorithm for the Housing Market Problem. In: Johnen, C., Schiller, E.M., Schmid, S. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2021. Lecture Notes in Computer Science(), vol 13046. Springer, Cham. https://doi.org/10.1007/978-3-030-91081-5_8

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  • DOI: https://doi.org/10.1007/978-3-030-91081-5_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-91080-8

  • Online ISBN: 978-3-030-91081-5

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