Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems - Fellows, M. R.; Knauer, C.; Nishimura, N.; Ragde, P.; Rosamond, F.; Stege, U.; Thilikos, D. M.; Whitesides, S. (Algorithmica, 2008)
We obtain faster algorithms for problems such as r -dimensional matching and r -set 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 ). This technique lets us combine Alon, Yuster and Zwick’s color-coding technique with dynamic programming to obtain faster fixed-parameter algorithms for these problems. Our algorithms run in time O ( n +2 O ( 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.