Power indices and easier hard problems

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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