On approximating four covering and packing problems

Mary Ashley, Tanya Berger-Wolf, Piotr Berman, Wanpracha Chaovalitwongse, Bhaskar DasGupta, Ming Yang Kao

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and have applications in biology ranging from full-sibling reconstructions in wild populations to biomolecular clusterings; however, as this paper shows, their approximability properties differ considerably. Our inapproximability constant for the triangle packing problem improves upon the previous results in [A. Caprara, R. Rizzi, Packing triangles in bounded degree graphs, Inform. Process. Lett. 84 (4) (2002) 175-180; J. Chlebíková, M. Chlebík, Complexity of approximating bounded variants of optimization problems, Theoret. Comput. Sci. 354 (3) (2006) 320-338]; this is done by directly transforming the inapproximability gap of Håstad for the problem of maximizing the number of satisfied equations for a set of equations over GF(2) [J. Håstad, Some optimal inapproximability results, in: Proc. of the 29th Annual ACM Symp. on Theory of Computing, 1997, pp. 1-10] and is interesting in its own right. Our approximability results on the full siblings reconstruction problems answers questions originally posed by Berger-Wolf et al. [T.Y. Berger-Wolf, B. DasGupta, W. Chaovalitwongse, M.V. Ashley, Combinatorial reconstruction of sibling relationships, in: Proc. of the 6th International Symposium on Computational Biology and Genome Informatics, 2005, pp. 1252-1255; T.Y. Berger-Wolf, S. Sheikh, B. DasGupta, M.V. Ashley, I. Caballero, W. Chaovalitwongse, S.L. Putrevu, Reconstructing sibling relationships in wild populations, Bioinformatics 23 (13) (2007) i49-i56] and our results on the maximum profit coverage problem provides almost matching upper and lower bounds on the approximation ratio, answering a question posed by Hassin and Or [R. Hassin, E. Or, A maximum profit coverage algorithm with application to small molecules cluster identification, in: 5th International Workshop Experimental Algorithms, in: Lecture Notes in Comput. Sci., vol. 4007, Springer-Verlag, 2006, pp. 265-276].

    Original languageEnglish (US)
    Pages (from-to)287-302
    Number of pages16
    JournalJournal of Computer and System Sciences
    Volume75
    Issue number5
    DOIs
    StatePublished - Aug 1 2009

    Fingerprint

    Covering Problem
    Packing Problem
    Inapproximability
    Approximability
    Profitability
    Coverage
    Profit
    Triangle
    Packing
    Bioinformatics
    Set Cover
    Computational Biology
    Genes
    Annual
    Biology
    Upper and Lower Bounds
    Genome
    Molecules
    Clustering
    Optimization Problem

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Networks and Communications
    • Computational Theory and Mathematics
    • Applied Mathematics

    Cite this

    Ashley, M., Berger-Wolf, T., Berman, P., Chaovalitwongse, W., DasGupta, B., & Kao, M. Y. (2009). On approximating four covering and packing problems. Journal of Computer and System Sciences, 75(5), 287-302. https://doi.org/10.1016/j.jcss.2009.01.002
    Ashley, Mary ; Berger-Wolf, Tanya ; Berman, Piotr ; Chaovalitwongse, Wanpracha ; DasGupta, Bhaskar ; Kao, Ming Yang. / On approximating four covering and packing problems. In: Journal of Computer and System Sciences. 2009 ; Vol. 75, No. 5. pp. 287-302.
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    abstract = "In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and have applications in biology ranging from full-sibling reconstructions in wild populations to biomolecular clusterings; however, as this paper shows, their approximability properties differ considerably. Our inapproximability constant for the triangle packing problem improves upon the previous results in [A. Caprara, R. Rizzi, Packing triangles in bounded degree graphs, Inform. Process. Lett. 84 (4) (2002) 175-180; J. Chleb{\'i}kov{\'a}, M. Chleb{\'i}k, Complexity of approximating bounded variants of optimization problems, Theoret. Comput. Sci. 354 (3) (2006) 320-338]; this is done by directly transforming the inapproximability gap of H{\aa}stad for the problem of maximizing the number of satisfied equations for a set of equations over GF(2) [J. H{\aa}stad, Some optimal inapproximability results, in: Proc. of the 29th Annual ACM Symp. on Theory of Computing, 1997, pp. 1-10] and is interesting in its own right. Our approximability results on the full siblings reconstruction problems answers questions originally posed by Berger-Wolf et al. [T.Y. Berger-Wolf, B. DasGupta, W. Chaovalitwongse, M.V. Ashley, Combinatorial reconstruction of sibling relationships, in: Proc. of the 6th International Symposium on Computational Biology and Genome Informatics, 2005, pp. 1252-1255; T.Y. Berger-Wolf, S. Sheikh, B. DasGupta, M.V. Ashley, I. Caballero, W. Chaovalitwongse, S.L. Putrevu, Reconstructing sibling relationships in wild populations, Bioinformatics 23 (13) (2007) i49-i56] and our results on the maximum profit coverage problem provides almost matching upper and lower bounds on the approximation ratio, answering a question posed by Hassin and Or [R. Hassin, E. Or, A maximum profit coverage algorithm with application to small molecules cluster identification, in: 5th International Workshop Experimental Algorithms, in: Lecture Notes in Comput. Sci., vol. 4007, Springer-Verlag, 2006, pp. 265-276].",
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    Ashley, M, Berger-Wolf, T, Berman, P, Chaovalitwongse, W, DasGupta, B & Kao, MY 2009, 'On approximating four covering and packing problems', Journal of Computer and System Sciences, vol. 75, no. 5, pp. 287-302. https://doi.org/10.1016/j.jcss.2009.01.002

    On approximating four covering and packing problems. / Ashley, Mary; Berger-Wolf, Tanya; Berman, Piotr; Chaovalitwongse, Wanpracha; DasGupta, Bhaskar; Kao, Ming Yang.

    In: Journal of Computer and System Sciences, Vol. 75, No. 5, 01.08.2009, p. 287-302.

    Research output: Contribution to journalArticle

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    AU - Ashley, Mary

    AU - Berger-Wolf, Tanya

    AU - Berman, Piotr

    AU - Chaovalitwongse, Wanpracha

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    AU - Kao, Ming Yang

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    N2 - In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and have applications in biology ranging from full-sibling reconstructions in wild populations to biomolecular clusterings; however, as this paper shows, their approximability properties differ considerably. Our inapproximability constant for the triangle packing problem improves upon the previous results in [A. Caprara, R. Rizzi, Packing triangles in bounded degree graphs, Inform. Process. Lett. 84 (4) (2002) 175-180; J. Chlebíková, M. Chlebík, Complexity of approximating bounded variants of optimization problems, Theoret. Comput. Sci. 354 (3) (2006) 320-338]; this is done by directly transforming the inapproximability gap of Håstad for the problem of maximizing the number of satisfied equations for a set of equations over GF(2) [J. Håstad, Some optimal inapproximability results, in: Proc. of the 29th Annual ACM Symp. on Theory of Computing, 1997, pp. 1-10] and is interesting in its own right. Our approximability results on the full siblings reconstruction problems answers questions originally posed by Berger-Wolf et al. [T.Y. Berger-Wolf, B. DasGupta, W. Chaovalitwongse, M.V. Ashley, Combinatorial reconstruction of sibling relationships, in: Proc. of the 6th International Symposium on Computational Biology and Genome Informatics, 2005, pp. 1252-1255; T.Y. Berger-Wolf, S. Sheikh, B. DasGupta, M.V. Ashley, I. Caballero, W. Chaovalitwongse, S.L. Putrevu, Reconstructing sibling relationships in wild populations, Bioinformatics 23 (13) (2007) i49-i56] and our results on the maximum profit coverage problem provides almost matching upper and lower bounds on the approximation ratio, answering a question posed by Hassin and Or [R. Hassin, E. Or, A maximum profit coverage algorithm with application to small molecules cluster identification, in: 5th International Workshop Experimental Algorithms, in: Lecture Notes in Comput. Sci., vol. 4007, Springer-Verlag, 2006, pp. 265-276].

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    Ashley M, Berger-Wolf T, Berman P, Chaovalitwongse W, DasGupta B, Kao MY. On approximating four covering and packing problems. Journal of Computer and System Sciences. 2009 Aug 1;75(5):287-302. https://doi.org/10.1016/j.jcss.2009.01.002