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.