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The Monotone Circuit Value Problem with Bounded Genus Is in NC

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Computing and Combinatorics (COCOON 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9797))

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Abstract

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].

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center “On-The-Fly Computing” (SFB 901) and the International Graduate School “Dynamic Intelligent Systems”.

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Acknowledgments

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

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Authors and Affiliations

  1. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Faisal N. Abu-Khzam

  2. Heinz Nixdorf Institute and Department of Computer Science, Paderborn University, Fürstenallee 11, 33102, Paderborn, Germany

    Shouwei Li, Friedhelm Meyer auf der Heide & Pavel Podlipyan

  3. Department of Mathematical Sciences, Haigazian University, Beirut, Lebanon

    Christine Markarian

  4. School of Engineering and Information Technology, Charles Darwin University, Darwin, Australia

    Faisal N. Abu-Khzam

Authors
  1. Faisal N. Abu-Khzam
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  2. Shouwei Li
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  3. Christine Markarian
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  4. Friedhelm Meyer auf der Heide
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  5. Pavel Podlipyan
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Corresponding author

Correspondence to Shouwei Li .

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Editors and Affiliations

  1. Virginia Commonwealth Univ , Richmond, Virginia, USA

    Thang N. Dinh

  2. University of Florida , Gainesville, Alabama, USA

    My T. Thai

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Abu-Khzam, F.N., Li, S., Markarian, C., Meyer auf der Heide, F., Podlipyan, P. (2016). The Monotone Circuit Value Problem with Bounded Genus Is in NC. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_8

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  • DOI: https://doi.org/10.1007/978-3-319-42634-1_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42633-4

  • Online ISBN: 978-3-319-42634-1

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