Abstract
A parameterized problem is fixed-parameter parallelizable (FPP) if it can be solved in O(f(k)⋅(logN)α) time using O(g(k)⋅Nβ) processors, where N is the input size, k is the parameter, f and g are arbitrary computable functions, and α, β are constants independent of N and k. We re-examine the k-vertex cover problem from a parameterized parallel complexity standpoint and present a parallel algorithm that outperforms the previous known algorithm: using O(m) instead of O(n2) processors, the running time improves from O(kk) to O(k3logn+1.2738k), where n and m are the number of vertices and edges of the input graph, respectively. This is achieved by first showing that vertex cover kernelization that is based on crown decomposition is in FPP as well. Finally, we consider the use of the recently introduced modular-width parameter. In particular, we show that the weighted maximum clique problem is FPP when parameterized by this auxiliary parameter.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.