On the Parameterized Parallel Complexity and the Vertex Cover Problem

F.N. Abu-Khzam, S. Li, C. Markarian, F. Meyer auf der Heide, P. Podlipyan, in: Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA), 2016, pp. 477–488.

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Efficiently parallelizable parameterized problems have been classified as being either in the class FPP (fixed-parameter parallelizable) or the class PNC (parameterized analog of NC), which contains FPP as a subclass. In this paper, we propose a more restrictive class of parallelizable parameterized problems called fixed-parameter parallel-tractable (FPPT). For a problem to be in FPPT, it should possess an efficient parallel algorithm not only from a theoretical standpoint but in practice as well. The primary distinction between FPPT and FPP is the parallel processor utilization, which is bounded by a polynomial function in the case of FPPT. We initiate the study of FPPT with the well-known k-vertex cover problem. In particular, we present a parallel algorithm that outperforms the best known parallel algorithm for this problem: using O(m) instead of O(n2) parallel processors, the running time improves from 4logn+O(kk) to O(k⋅log3n), where m is the number of edges, n is the number of vertices of the input graph, and k is an upper bound of the size of the sought vertex cover. We also note that a few P-complete problems fall into FPPT including the monotone circuit value problem (MCV) when the underlying graphs are bounded by a constant Euler genus.
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Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA)
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477-488
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Abu-Khzam FN, Li S, Markarian C, Meyer auf der Heide F, Podlipyan P. On the Parameterized Parallel Complexity and the Vertex Cover Problem. In: Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA). LNCS. ; 2016:477-488. doi:10.1007/978-3-319-48749-6_35
Abu-Khzam, F. N., Li, S., Markarian, C., Meyer auf der Heide, F., & Podlipyan, P. (2016). On the Parameterized Parallel Complexity and the Vertex Cover Problem. In Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA) (pp. 477–488). https://doi.org/10.1007/978-3-319-48749-6_35
@inproceedings{Abu-Khzam_Li_Markarian_Meyer auf der Heide_Podlipyan_2016, series={LNCS}, title={On the Parameterized Parallel Complexity and the Vertex Cover Problem}, DOI={10.1007/978-3-319-48749-6_35}, booktitle={Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA)}, author={Abu-Khzam, Faisal N. and Li, Shouwei and Markarian, Christine and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}, year={2016}, pages={477–488}, collection={LNCS} }
Abu-Khzam, Faisal N., Shouwei Li, Christine Markarian, Friedhelm Meyer auf der Heide, and Pavel Podlipyan. “On the Parameterized Parallel Complexity and the Vertex Cover Problem.” In Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA), 477–88. LNCS, 2016. https://doi.org/10.1007/978-3-319-48749-6_35.
F. N. Abu-Khzam, S. Li, C. Markarian, F. Meyer auf der Heide, and P. Podlipyan, “On the Parameterized Parallel Complexity and the Vertex Cover Problem,” in Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA), 2016, pp. 477–488.
Abu-Khzam, Faisal N., et al. “On the Parameterized Parallel Complexity and the Vertex Cover Problem.” Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA), 2016, pp. 477–88, doi:10.1007/978-3-319-48749-6_35.
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