, Volume 23, Issue 1, pp 209-225

Power indices and easier hard problems

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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.

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.