The Monotone Circuit Value Problem with Bounded Genus Is in NC

  • Faisal N. Abu-Khzam
  • Shouwei LiEmail author
  • Christine Markarian
  • Friedhelm Meyer auf der Heide
  • Pavel Podlipyan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)


We present an efficient parallel algorithm for the general Monotone Circuit Value Problem (MCVP) with n gates and an underlying graph of bounded genus k. Our algorithm generalizes a recent result by Limaye et al. who showed that MCVP with toroidal embedding (genus 1) is in NC when the input contains a toroidal embedding of the circuit. In addition to extending this result from genus 1 to any bounded genus k, and unlike the work reported by Limaye et al., we do not require a precomputed embedding to be given. Most importantly, our results imply that given a P-complete problem, it is possible to find an algorithm that makes the problem fall into NC by fixing one or more parameters. Hence, we deduce the interesting analogy: Fixed Parameter Parallelizable (FPP) is with respect to P-complete what Fixed Parameter Tractable (FPT) is with respect to NP-complete. Similar work that uses treewidth as parameter was also presented by Elberfeld et al. in [6].


Directed Acyclic Graph Sink Node Vertex Cover Input Graph Layer Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We wish to thank the anonymous referees for their valuable comments to improve the structure and presentation of this paper.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Faisal N. Abu-Khzam
    • 1
    • 4
  • Shouwei Li
    • 2
    Email author
  • Christine Markarian
    • 3
  • Friedhelm Meyer auf der Heide
    • 2
  • Pavel Podlipyan
    • 2
  1. 1.Department of Computer Science and MathematicsLebanese American UniversityBeirutLebanon
  2. 2.Heinz Nixdorf Institute and Department of Computer SciencePaderborn UniversityPaderbornGermany
  3. 3.Department of Mathematical SciencesHaigazian UniversityBeirutLebanon
  4. 4.School of Engineering and Information TechnologyCharles Darwin UniversityDarwinAustralia

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