Assertion: exponential time hypothesis | /r/HasProperty | true
Facets:
Source sentences:
text: Therefore, if the exponential time hypothesis is true, there must be infinitely many values of k for which s k differs from s k + 1 .
text: If cliques or independent sets of logarithmic size could be found in polynomial time, the exponential time hypothesis would be false.
text: Equivalently, if s k > 0 for any k > 3, then s 3 > 0 as well, and the exponential time hypothesis would be true.
text: Therefore, if the strong exponential time hypothesis is true, then there would be no algorithm for general CNF satisfiability that is significantly faster than testing all possible truth assignments.
text: In particular, if the strong exponential time hypothesis is true, then the optimal time bound for finding independent sets on graphs of treewidth w is (2 − o(1))wnO(1), the optimal time for the dominating set problem is (3 − o(1))wnO(1), the optimum time for maximum cut is (2 − o(1))wnO(1), and the optimum time for k-coloring is (k − o(1))wnO(1).
text: If the exponential time hypothesis is true, then 3-SAT would not have a polynomial time algorithm, and therefore it would follow that P ≠ NP.
text: There exist NP-complete problems for which the best known running times have the form O(2nc) for c < 1, and if the best possible running time for 3-SAT were of this form, then P would be unequal to NP (because 3-SAT is NP-complete and this time bound is not polynomial) but the exponential time hypothesis would be false.