conference paper
On the Parameterized Parallel Complexity and the Vertex Cover Problem
Faisal N.
Abu-Khzam
author
Shouwei
Li
author
Christine
Markarian
author 37612
Friedhelm
Meyer auf der Heide
author 15523
Pavel
Podlipyan
author
63
department
SFB 901
project
SFB 901 - Subprojekt A1
project
SFB 901 - Project Area A
project
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.
https://ris.uni-paderborn.de/download/177/5266/OnTheParameterizedParallelComp.pdf
application/pdf
2016
eng
Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA)10.1007/978-3-319-48749-6_35
477-488
@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={<a href="https://doi.org/10.1007/978-3-319-48749-6_35">10.1007/978-3-319-48749-6_35</a>}, 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 <i>Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA)</i>, 477–88. LNCS, 2016. <a href="https://doi.org/10.1007/978-3-319-48749-6_35">https://doi.org/10.1007/978-3-319-48749-6_35</a>.
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 <i>Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA)</i> (pp. 477–488). <a href="https://doi.org/10.1007/978-3-319-48749-6_35">https://doi.org/10.1007/978-3-319-48749-6_35</a>
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: <i>Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA)</i>. LNCS. ; 2016:477-488. doi:<a href="https://doi.org/10.1007/978-3-319-48749-6_35">10.1007/978-3-319-48749-6_35</a>
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.
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 <i>Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA)</i>, 2016, pp. 477–488.
Abu-Khzam, Faisal N., et al. “On the Parameterized Parallel Complexity and the Vertex Cover Problem.” <i>Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA)</i>, 2016, pp. 477–88, doi:<a href="https://doi.org/10.1007/978-3-319-48749-6_35">10.1007/978-3-319-48749-6_35</a>.
1772017-10-17T12:41:26Z2019-01-03T13:12:13Z