Abstract
Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account that when we only have a small number of processors (between 2 and, say, 1024), it is more important that the parallel algorithms are work-efficient. In the present paper we investigate how work-efficient fpt algorithms can be designed. We review standard methods from fpt theory, like kernelization, search trees, and interleaving, and prove trade-offs for them between work efficiency and runtime improvements. This results in a toolbox for developing work-efficient parallel fpt algorithms.
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Notes
- 1.
Of course, we actually branch on a vertex of degree at least 3, meaning that \(D = \{(1,3); (1,4); (1,5); \dots \}\) holds, but \(d = (1,3)\) clearly leads to the largest and deepest search trees and it suffices to only consider this “worst d.”.
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Bannach, M., Skambath, M., Tantau, T. (2019). Towards Work-Efficient Parallel Parameterized Algorithms. In: Das, G., Mandal, P., Mukhopadhyaya, K., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science(), vol 11355. Springer, Cham. https://doi.org/10.1007/978-3-030-10564-8_27
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