Approximation algorithms for the maximum power consumption problem on combinatorial circuits

Abstract

The maximum power consumption problem on combinatorial circuits is the problem of estimating the maximum power consumption of a given combinatorial circuit. It is easy to see that this problem for general circuits is hard to approximate within a factor of m1−ε, where m is the number of gates in an input circuit and ε is any positive (small) constant. In this paper, we consider restricted circuits, namely, those consisting of only one level of AND/OR gates. Then the problem becomes a kind of MAX 2SAT where each variable takes one of four values, f, t, d and u. This problem is NP-hard and the main objective of this paper is to give approximation algorithms. We consider two cases, the case that positive and negative appearances of each variable are well balanced and the general case. For the first case, we achieve an approximation ratio of (formula presented) where α = 0:87856 and k (formula presented) is the maximum ratio of the number of positive appearances over the number of negative appearances of each variable. For the general case, we obtain an approximation ratio of 1.7. Both results involve deep, systematic analyses.