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International Computing and Combinatorics Conference

COCOON 2016: Computing and Combinatorics pp 92–102Cite as

The Monotone Circuit Value Problem with Bounded Genus Is in NC

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

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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References

  1. Battle, J., Harary, F., Kodama, Y.: Additivity of the genus of a graph. Bull. Am. Math. Soc. 68(6), 565–568 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  2. Booth, K.S., Lueker, G.S.: Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comput. Syst. Sci. 13(3), 335–379 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cesati, M., Di Ianni, M.: Parameterized parallel complexity. In: Pritchard, D., Reeve, J.S. (eds.) Euro-Par 1998. LNCS, vol. 1470, pp. 892–896. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  4. Chen, J., Kanj, I.A., Xia, G.: Improved upper bounds for vertex cover. Theor. Comput. Sci. 411(40), 3736–3756 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cook, S.A.: A taxonomy of problems with fast parallel algorithms. Inf. Control 64(1), 2–22 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  6. Elberfeld, M., Jakoby, A., Tantau, T.: Logspace versions of the theorems of bodlaender and courcelle. In: 2010 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 143–152. IEEE (2010)

    Google Scholar 

  7. Goldschlager, L.M.: The monotone and planar circuit value problems are log space complete for P. SIGACT News 9(2), 25–29 (1977)

    Article  MATH  Google Scholar 

  8. Klein, P.N., Reif, J.H.: An efficient parallel algorithm for planarity. J. Comput. Syst. Sci. 37(2), 190–246 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ladner, R.E.: The circuit value problem is log space complete for P. SIGACT News 7(1), 18–20 (1975)

    Article  MathSciNet  Google Scholar 

  10. Limaye, N., Mahajan, M., Sarma, J.M.: Upper bounds for monotone planar circuit value and variants. Comput. Complex. 18(3), 377–412 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ramachandran, V., Yang, H.: An efficient parallel algorithm for the general planar monotone circuit value problem. SIAM J. Comput. 25(2), 312–339 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  12. Tarjan, R.E., Vishkin, U.: An efficient parallel biconnectivity algorithm. SIAM J. Comput. 14(4), 862–874 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  13. Yang, H.: An NC algorithm for the general planar monotone circuit value problem. In: Proceedings of the Third IEEE Symposium on Parallel and Distributed Processing, pp. 196–203, December 1991

    Google Scholar 

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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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© 2016 Springer International Publishing Switzerland

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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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