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Power indices and easier hard problems. (English) Zbl 0719.68025
For a computational problem A let I(A) be the set of real numbers $$\{\alpha| A\in DTIME(2^{n\alpha})\}$$. Define power-index(A) to be the greatest lower bound of I(A). The authors make the following satisfiability hypothesis: power-index(SAT)$$=1$$, and use it to characterize the power index of many other NP-complete problems. For instance, it is shown that power index of CLIQUE and PARTITION is 1/2.
In addition, the authors introduce the notion of structure tree for a given CNF formula. They use the structure tree, together with separator arguments, to show that a 3CNF formula F can be tested for satisfiability in time $$| F| \cdot v^{o(\sqrt{v+c})}$$, where v is the number of variables in F and c is the maximum number of crossovers needed in a planar layout of F.
Reviewer: G.Slutzki (Ames)

MSC:
 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.) 68Q25 Analysis of algorithms and problem complexity
PARTITION
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