Approximability of Minimum AND-Circuits

  • Jan Arpe
  • Bodo Manthey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)


Given a set of monomials, the Minimum-AND-Circuit problem asks for a circuit that computes these monomials using AND-gates of fan-in two and being of minimum size. We prove that the problem is not polynomial time approximable within a factor of less than 1.0051 unless P = NP, even if the monomials are restricted to be of degree at most three. For the latter case, we devise several efficient approximation algorithms, yielding an approximation ratio of 1.278. For the general problem, we achieve an approximation ratio of d–3/2, where d is the degree of the largest monomial. In addition, we prove that the problem is fixed parameter tractable with the number of monomials as parameter. Finally, we reveal connections between the Minimum AND-Circuit problem and several problems from different areas.


Approximation Ratio Vertex Cover Input Instance Addition Chain Input Gate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jan Arpe
    • 1
  • Bodo Manthey
    • 2
  1. 1.Institut für Theoretische InformatikUniversität zu LübeckLübeckGermany
  2. 2.InformatikUniversität des SaarlandesSaarbrückenGermany

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