论文信息 - Approximating a generalization of MAX 2SAT and MIN 2SAT

Approximating a generalization of MAX 2SAT and MIN 2SAT

Abstract This paper considers generalized 2SAT problems, MAX GEN2SAT and MIN GEN2SAT . Instances of these problems are defined on a collection of “clauses”, which we refer to as genclauses . A genclause is any boolean function on two variables, and each genclause has a non-negative weight associated with it in the problems that are considered. The objective of MAX GEN2SAT ( MIN GEN2SAT ) is to select a truth assignment that maximizes (minimizes) the total weight of satisfied genclauses. Goemans and Williamson (J. ACM 42(6) (1995) 1115–1145) used semidefinite programming and were able to provide substantial improvements in approximation factor guarantee for several important problems: MAX 2SAT , MAX CUT , MAX DICUT . In this paper we show how their approximation technique can be used to yield an approximation algorithm for MAX GEN2SAT , for which MAX 2SAT , MAX CUT , MAX DICUT are special cases. For MIN GEN2SAT , employing a recent technique of Hochbaum (Manuscript, UC Berkeley, June 1997) leads to easy recognition of which instances are polynomial or 2-approximable. The polynomial instances of MIN GEN2SAT have corresponding instances of MAX GEN2SAT which are thus identified as solvable in polynomial time. Among the applications of the approximation algorithms described it is shown that the forest harvesting problem has a 0.87856-approximation algorithm.

Dorit S. Hochbaum | Anu Pathria

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