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Hard Instances of Hard Problems

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STACS 2000 (STACS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1770))

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Abstract

This paper investigates the instance complexities of problems that are hard or weakly hard for exponential time under polynomial time, many-one reductions. It is shown that almost every instance of almost every problem in exponential time has essentially maximal instance complexity. It follows that every weakly hard problem has a dense set of such maximally hard instances. This extends the theorem, due to Orponen, Ko, Schöning and Watanabe (1994), that every hard problem for exponential time has a dense set of maximally hard instances. Complementing this, it is shown that every hard problem for exponential time also has a dense set of unusually easy instances.

This research was supported in part by National Science Foundation Grant CCR9610461.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Iowa State University, Ames, Iowa, 50011, USA

    Jack H. Lutz, Vikram Mhetre & Sridhar Srinivasan

Authors
  1. Jack H. Lutz
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  2. Vikram Mhetre
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  3. Sridhar Srinivasan
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dept. of Theoretical Computer Science, Universität Dresden, 01062, Dresden, Germany

    Horst Reichel

  2. Université de Lille, LIFL - UPRESA 8022, CNRS, Bât. M3 - UFR IEEA, 59655, Villeneuve d’ASCQ Cedex, France

    Sophie Tison

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Lutz, J.H., Mhetre, V., Srinivasan, S. (2000). Hard Instances of Hard Problems. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_27

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  • DOI: https://doi.org/10.1007/3-540-46541-3_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67141-1

  • Online ISBN: 978-3-540-46541-6

  • eBook Packages: Springer Book Archive

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