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Power indices and easier hard problems

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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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Authors and Affiliations

  1. Department of Computer Science, State University of New York at Albany, 12222, Albany, NY, USA

    R. E. Stearns & H. B. Hunt III

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  1. R. E. Stearns
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  2. H. B. Hunt III
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Additional information

The research of R. E. Stearns was supported by NSF Grants DCR 83-03932 and CCR 89-03319, and that of H. B. Hunt was supported by NSF Grants DCR 86-03184 and CCR 89-03319.

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Stearns, R.E., Hunt, H.B. Power indices and easier hard problems. Math. Systems Theory 23, 209–225 (1990). https://doi.org/10.1007/BF02090776

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