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International Computing and Combinatorics Conference

COCOON 2014: Computing and Combinatorics pp 25–36Cite as

L  ∞ -Discrepancy Analysis of Polynomial-Time Deterministic Samplers Emulating Rapidly Mixing Chains

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8591))

Abstract

Markov chain Monte Carlo (MCMC) is a standard technique to sample from a target distribution by simulating Markov chains. In an analogous fashion to MCMC, this paper proposes a deterministic sampling algorithm based on deterministic random walk, such as the rotor-router model (a.k.a. Propp machine). For the algorithm, we give an upper bound of the point-wise distance (i.e., infinity norm) between the “distributions” of a deterministic random walk and its corresponding Markov chain in terms of the mixing time of the Markov chain. As a result, for uniform sampling of #P-complete problems, such as 0-1 knapsack solutions, linear extensions, matchings, etc., for which rapidly mixing chains are known, our deterministic algorithm provides samples with a “distribution” with a point-wise distance at most ε from the target distribution, in time polynomial in the input size and ε − 1.

This manuscript is an extended abstract version of [19].

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Authors and Affiliations

  1. Graduate School of Information Science and Electrical Engineering, Kyushu University, Japan

    Takeharu Shiraga, Yukiko Yamauchi, Shuji Kijima & Masafumi Yamashita

Authors
  1. Takeharu Shiraga
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  2. Yukiko Yamauchi
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  3. Shuji Kijima
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  4. Masafumi Yamashita
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1410, 30303, Atlanta, GA, USA

    Zhipeng Cai

  2. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1443, 30303, Atlanta, GA, USA

    Alex Zelikovsky

  3. Department of Computer Science, Georgia State University, 34 Peachtree Street, Suite 1449, 30303, Atlanta, GA, USA

    Anu Bourgeois

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Shiraga, T., Yamauchi, Y., Kijima, S., Yamashita, M. (2014). L  ∞ -Discrepancy Analysis of Polynomial-Time Deterministic Samplers Emulating Rapidly Mixing Chains. In: Cai, Z., Zelikovsky, A., Bourgeois, A. (eds) Computing and Combinatorics. COCOON 2014. Lecture Notes in Computer Science, vol 8591. Springer, Cham. https://doi.org/10.1007/978-3-319-08783-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-08783-2_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08782-5

  • Online ISBN: 978-3-319-08783-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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