{"abstract":[{"text":"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.","lang":"eng"}],"doi":"10.1007/978-3-319-48749-6_35","file_date_updated":"2018-11-02T14:15:18Z","year":"2016","status":"public","user_id":"477","project":[{"name":"SFB 901","_id":"1"},{"_id":"5","name":"SFB 901 - Subprojekt A1"},{"_id":"2","name":"SFB 901 - Project Area A"}],"_id":"177","type":"conference","language":[{"iso":"eng"}],"department":[{"_id":"63"}],"ddc":["000"],"title":"On the Parameterized Parallel Complexity and the Vertex Cover Problem","date_updated":"2022-01-06T06:53:17Z","publication":"Proceedings of the 10th International Conference on Combinatorial Optimization and Applications (COCOA)","author":[{"full_name":"Abu-Khzam, Faisal N.","last_name":"Abu-Khzam","first_name":"Faisal N."},{"full_name":"Li, Shouwei","last_name":"Li","first_name":"Shouwei"},{"id":"37612","first_name":"Christine","last_name":"Markarian","full_name":"Markarian, Christine"},{"first_name":"Friedhelm","id":"15523","full_name":"Meyer auf der Heide, Friedhelm","last_name":"Meyer auf der Heide"},{"last_name":"Podlipyan","full_name":"Podlipyan, Pavel","first_name":"Pavel"}],"page":"477-488","file":[{"content_type":"application/pdf","file_id":"5266","relation":"main_file","success":1,"file_size":293345,"file_name":"OnTheParameterizedParallelComp.pdf","creator":"ups","date_updated":"2018-11-02T14:15:18Z","access_level":"closed","date_created":"2018-11-02T14:15:18Z"}],"series_title":"LNCS","citation":{"apa":"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","ama":"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","mla":"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.","bibtex":"@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} }","ieee":"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.","short":"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.","chicago":"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."},"has_accepted_license":"1","date_created":"2017-10-17T12:41:26Z"}