Faster Exact Solutions for Some NP-Hard Problems

This paper considers a number of NP-complete problems, and provides faster algorithms for solving them. The solutions are based on a recursive partitioning of the problem domain, and careful elimination of some of the branches along the search without actually checking them. The time complexity of the proposed algorithms is of the form O(2 ) for constant 0¡ ¡ 1, where n is the output size of the problem. In particular, such algorithms are presented for the Exact SAT and Exact Hitting Set problems (with =0:3212), and for the Exact 3SAT problem (with =0:2072). Both algorithms improve on previous ones proposed in the literature. c © 2002 Elsevier Science B.V. All rights reserved.