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This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many… Expand
For more than 40 years, Branch & Reduce exponential-time backtracking algorithms have been among the most common tools used for finding exact solutions of NP-hard problems. Despite that, the way to… Expand
Graph minors theory, developed by Robertson & Seymour, provides a list of powerful theoretical results and tools. However, the wide spread opinion in Graph Algorithms community about this theory is… Expand
Discovering surprises in the face of intractability.
Polynomial time preprocessing to reduce instance size is one of the most commonly deployed heuristics to tackle computationally hard problems. In a parameterized problem, every instance I comes with… Expand
We give two algorithms computing representative families of linear and uniform matroids and demonstrate how to use representative families for designing single-exponential parameterized and exact… Expand
Davis-Putnam-style exponential-time backtracking algorithms are the most common algorithms used for finding exact solutions of NP-hard problems. The analysis of such recursive algorithms is based on… Expand
We present improved parameterized algorithms for the Feedback Vertex Set problem on both unweighted and weighted graphs. Both algorithms run in time O(5kkn2). The algorithms construct a feedback… Expand
We present improved parameterized algorithms for the feedback vertex set problem on both unweighted and weighted graphs. Both algorithms run in time O(5^kkn^2). The algorithms construct a feedback… Expand
A proper coloring of a graph G is equitable if the sizes of any two color classes differ by at most one. A proper coloring is l-bounded, when each color class has size at most l. We consider the… Expand