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 + 2O(k) ), an improvement over previous algorithms for some of these problems running in time O(n + kO(k) ). The flexibility of our approach allows tuning of algorithms to obtain smaller constants in the exponent.

• Type: Conference
• Year: 2004
• Where: ESA
• Authors: Michael R. Fellows, Christian Knauer, Naomi Nishimura, Prabhakar Ragde, Frances A. Rosamond, Ulrike Stege, Dimitrios M. Thilikos, Sue Whitesides
• Keywords: Algorithms, ESA 2004, Faster Algorithms, Graph Edge Packing