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Sparse Sets, Approximable Sets, and Parallel Queries to NP

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STACS 99 (STACS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1563))

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Abstract

We show that if an NP-complete set or a coNP-complete set is polynomial-time disjunctive truth-table reducible to a sparse set then FP NP∥ = FPNP[log]. Similarly, we show that if SAT is O(log n)-approximable then FP NP∥ = FPNP[log]. Since FP NP∥ = FPNP[log] implies that SAT is O(log n)-approximable [BFT97], it follows from our result that these two hypotheses are equivalent. We also show that if an NP-complete set or a coNP-complete set is disjunctively reducible to a sparse set of polylogarithmic density then, in fact, P = NP.

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Author information

Authors and Affiliations

  1. Institute of Mathematical Sciences, C. I. T. Campus, Chennai, 600 113, India

    Vikraman Arvind

  2. Abteilung Theoretische Informatik, Universität Ulm, D-89069, Ulm, Germany

    Jacobo Torán

Authors
  1. Vikraman Arvind
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  2. Jacobo Torán
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Editor information

Editors and Affiliations

  1. FB IV - Informatik, Universität Trier, D-54286, Trier, Germany

    Christoph Meinel

  2. LIFL, Université de Lille I, Bătiment 3, F-59655, Villeneuve d’Ascq Cedex, France

    Sophie Tison

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© 1999 Springer-Verlag Berlin Heidelberg

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Arvind, V., Torán, J. (1999). Sparse Sets, Approximable Sets, and Parallel Queries to NP. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_26

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  • DOI: https://doi.org/10.1007/3-540-49116-3_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65691-3

  • Online ISBN: 978-3-540-49116-3

  • eBook Packages: Springer Book Archive

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