Approximation hardness of bounded degree MIN-CSP and MIN-BISECTION

Piotr Berman, Marek Karpinski

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    11 Scopus citations

    Abstract

    We consider bounded occurrence (degree) instances of a minimum constraint satisfaction problem MIN-LIN2 and a MINBISECTION problem for graphs. MIN-LIN2 is an optimization problem for a given system of linear equations mod 2 to construct a solution that satisfies the minimum number of them. E3-OCC-MIN-E3-LIN2 is the bounded occurrence (degree) problem restricted as follows: each equation has exactly 3 variables and each variable occurs in exactly 3 equations. Clearly, MIN-LIN2 is equivalent to another well known problem, the Nearest Codeword problem, and E3-OCC-MIN-E3-LIN2 to its bounded occurrence version. MIN-BISECTION is a problem of findinga minimum bisection of a graph, while 3-MIN-BISECTION is the MIN-BISECTION problem restricted to 3-regular graphs only. We show that, somewhat surprisingly, these two restricted problems are exactly as hard to approximate as their general versions. In particular, an approximation ratio lower bound for E3-OCC-MIN-E3-LIN2 (bounded 3-occurrence 3-ary Nearest Codeword problem) is equal to MIN-LIN2 (Nearest Codeword problem) lower bound nΩ(1)/ log log n. Moreover, an existence of a constant factor approximation ratio (or a PTAS) for 3-MIN-BISECTION entails existence of a constant approximation ratio (or a PTAS) for the general MIN-BISECTION.

    Original languageEnglish (US)
    Title of host publicationAutomata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings
    Pages623-632
    Number of pages10
    Publication statusPublished - Dec 1 2002
    Event29th International Colloquium on Automata, Languages, and Programming, ICALP 2002 - Malaga, Spain
    Duration: Jul 8 2002Jul 13 2002

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume2380 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other29th International Colloquium on Automata, Languages, and Programming, ICALP 2002
    CountrySpain
    CityMalaga
    Period7/8/027/13/02

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    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Berman, P., & Karpinski, M. (2002). Approximation hardness of bounded degree MIN-CSP and MIN-BISECTION. In Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings (pp. 623-632). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2380 LNCS).