The Monotone Circuit Value Problem with Bounded Genus Is in NC
F.N. Abu-Khzam, S. Li, C. Markarian, F. Meyer auf der Heide, P. Podlipyan, in: Proceedings of the 22nd International Conference on Computing and Combinatorics (COCOON), 2016, pp. 92–102.
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Abu-Khzam, Faisal N. ;
Li, Shouwei;
Markarian, ChristineLibreCat;
Meyer auf der Heide, FriedhelmLibreCat;
Podlipyan, Pavel
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].
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Proceedings Title
Proceedings of the 22nd International Conference on Computing and Combinatorics (COCOON)
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LNCS
Page
92-102
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Cite this
Abu-Khzam FN, Li S, Markarian C, Meyer auf der Heide F, Podlipyan P. The Monotone Circuit Value Problem with Bounded Genus Is in NC. In: Proceedings of the 22nd International Conference on Computing and Combinatorics (COCOON). LNCS. ; 2016:92-102. doi:10.1007/978-3-319-42634-1_8
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 Proceedings of the 22nd International Conference on Computing and Combinatorics (COCOON) (pp. 92–102). https://doi.org/10.1007/978-3-319-42634-1_8
@inproceedings{Abu-Khzam_Li_Markarian_Meyer auf der Heide_Podlipyan_2016, series={LNCS}, title={The Monotone Circuit Value Problem with Bounded Genus Is in NC}, DOI={10.1007/978-3-319-42634-1_8}, booktitle={Proceedings of the 22nd International Conference on Computing and Combinatorics (COCOON)}, author={Abu-Khzam, Faisal N. and Li, Shouwei and Markarian, Christine and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}, year={2016}, pages={92–102}, collection={LNCS} }
Abu-Khzam, Faisal N. , Shouwei Li, Christine Markarian, Friedhelm Meyer auf der Heide, and Pavel Podlipyan. “The Monotone Circuit Value Problem with Bounded Genus Is in NC.” In Proceedings of the 22nd International Conference on Computing and Combinatorics (COCOON), 92–102. LNCS, 2016. https://doi.org/10.1007/978-3-319-42634-1_8.
F. N. Abu-Khzam, S. Li, C. Markarian, F. Meyer auf der Heide, and P. Podlipyan, “The Monotone Circuit Value Problem with Bounded Genus Is in NC,” in Proceedings of the 22nd International Conference on Computing and Combinatorics (COCOON), 2016, pp. 92–102.
Abu-Khzam, Faisal N., et al. “The Monotone Circuit Value Problem with Bounded Genus Is in NC.” Proceedings of the 22nd International Conference on Computing and Combinatorics (COCOON), 2016, pp. 92–102, doi:10.1007/978-3-319-42634-1_8.
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