Mathematical systems theory

, Volume 23, Issue 1, pp 209–225

Power indices and easier hard problems

  • R. E. Stearns
  • H. B. HuntIII
Article

Abstract

The concepts of power_index, satisfiability hypothesis (SH), and structure tree are introduced and used to make sharper hypotheses about a problem's complexity than “the problem isNP-complete.” These concepts are used to characterize the complexities of a number of basicNP-complete problems, including both CLIQUE and PARTITION which are shown to have power-indices at most 1/2. Also, the problem 3SAT is shown to be solvable deterministically in time exponential only in thesquare root ofv+c, wherev is the number of variables andc is the number of “crossovers” needed to layout the formula in the plane.

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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • R. E. Stearns
    • 1
  • H. B. HuntIII
    • 1
  1. 1.Department of Computer ScienceState University of New York at AlbanyAlbanyUSA

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