Abstract
We obtain faster algorithms for problems such as r-dimensional matching, r-set packing, graph packing, and graph edge packing when the size k of the solution is considered a parameter. We first establish a general framework for finding and exploiting small problem kernels (of size polynomial in k). Previously such a kernel was known only for triangle packing. This technique lets us combine, in a new and sophisticated way, Alon, Yuster and Zwick’s color-coding technique with dynamic programming on the structure of the kernel to obtain faster fixed-parameter algorithms for these problems. Our algorithms run in time O(n+2O(k)), an improvement over previous algorithms for some of these problems running in time O(n+k O(k)). The flexibility of our approach allows tuning of algorithms to obtain smaller constants in the exponent.
Research initiated at the International Workshop on Fixed Parameter Tractability in Computational Geometry and Games, Bellairs Research Institute of McGill University, Holetown, Barbados, Feb. 7-13, 2004, organized by S. Whitesides.
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Fellows, M.R. et al. (2004). Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_29
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DOI: https://doi.org/10.1007/978-3-540-30140-0_29
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