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Power indices and easier hard problems
 R. E. Stearns,
 H. B. Hunt III
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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 isNPcomplete.” These concepts are used to characterize the complexities of a number of basicNPcomplete problems, including both CLIQUE and PARTITION which are shown to have powerindices 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 8303932 and CCR 8903319, and that of H. B. Hunt was supported by NSF Grants DCR 8603184 and CCR 8903319.
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 Title
 Power indices and easier hard problems
 Journal

Mathematical systems theory
Volume 23, Issue 1 , pp 209225
 Cover Date
 19901201
 DOI
 10.1007/BF02090776
 Print ISSN
 00255661
 Online ISSN
 14330490
 Publisher
 SpringerVerlag
 Additional Links
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 Industry Sectors
 Authors

 R. E. Stearns ^{(1)}
 H. B. Hunt III ^{(1)}
 Author Affiliations

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