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

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Abstract

In this paper, we prove under a plausible complexity hypothesis that Reduced Error Pruning of branching programs is hard to approximate within log1−δn, 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.

References (14)

  • Y. Mansour et al.

    Boosting using branching programs

    J. Comput. System Sci.

    (2002)
  • L. Breiman et al.

    Classification and Regression Trees

    (1984)
  • N.H. Bshouty et al.

    On learning width two branching programs

  • T. Elomaa et al.

    An analysis of reduced error pruning

    J. Artificial Intelligence Res.

    (2001)
  • T. Elomaa et al.

    The difficulty of reduced error pruning of leveled branching programs

    Ann. Math. Artificial Intelligence

    (2003)
  • U. Feige

    A threshold of lnn for approximating set cover

    J. ACM

    (1998)
  • U. Feige et al.

    Approximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT

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