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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| مؤلفون آخرون: | , , , |
| التنسيق: | conferenceObject |
| منشور في: |
2016
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| 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. |
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