Abstract 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 colorcoding technique with dynamic programming to obtain faster fixed-parameter algo- rithms 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
