Reduced Error Pruning of branching programs cannot be approximated to within a logarithmic factor

Richard Nock, Tapio Elomaa, Matti Kääriäinen

Abstract: In this paper, we prove under a plausible complexity hypothesis that Reduced Error Pruning of branching programs is hard to approximate within log 1− δ n , for every δ >0, where n is the number of description variables, a measure of the problem's complexity. The result holds under the assumption that NP problems do not admit deterministic, slightly superpolynomial time algorithms: NP⊄TIME(| I | O(loglog| I |) ). This improves on a previous result that only had a small constant inapproximability ratio, and puts a fairly strong constraint on the efficiency of potential approximation algorithms. The result also holds for read-once and μ -branching programs.