מירב זהבי

Narrow sieves, representative sets and divide-and-color are three breakthrough techniques related to color coding, which led to the design of extremely fast parameterized algorithms. We present a novel family of strategies for applying mixtures of them. This includes: (a) a mix of representative sets and narrow sieves; (b) a faster computation of representative sets under certain separateness conditions, mixed with divide-and-color and a new technique, called “balanced cutting”; (c) two mixtures of representative sets and a new technique, called “unbalanced cutting”. We demonstrate our strategies by obtaining, among other results, significantly faster algorithms for k-Internal Out-Branching and Weighted 3-Set k-Packing, and a general framework for speedingup the previous best deterministic algorithms for k-Path, k-Tree, r- Dimensional k-Matching, Graph Motif and Partial Cover.