Faster fixed-parameter tractable algorithms for matching and packing problems. In:

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

Faster fixed-parameter tractable algorithms for matching and packing problems

Abstract. We obtain faster algorithms for problems such as rdimensional 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 +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.

Faster fixed-parameter tractable algorithms for matching and packing problems

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