On the parameterized parallel complexity and the vertex cover problem

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...

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محفوظ في:
التفاصيل البيبلوغرافية
المؤلف الرئيسي: Abu-Khzam, Faisal N. (author)
مؤلفون آخرون: Li, Shouwei (author), Markarian, Chrisitne (author), Meyer auf der Heide, Friedhelm (author), Podipyan, PAvel (author)
التنسيق: conferenceObject
منشور في: 2016
الوصول للمادة أونلاين:http://hdl.handle.net/10725/7519
http://dx.doi.org/10.1007/978-3-319-48749-6 35
http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php
https://link.springer.com/chapter/10.1007%2F978-3-319-48749-6_35
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الملخص: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.