Greedy Localization, Iterative Compression, Modeled Crown Reductions: New FPT Techniques, an Improved Algorithm for Set Splitting, and a Novel 2k Kernelization for Vertex Cover
نویسندگان
چکیده
The two objectives of this paper are: (1) to articulate three new general techniques for designing FPT algorithms, and (2) to apply these to obtain new FPT algorithms for Set Splitting and Vertex Cover. In the case of Set Splitting, we improve the best previous O(72) FPT algorithm due to Dehne, Fellows and Rosamond [DFR03], to O(8) by an approach based on greedy localization in conjunction with modeled crown reduction. In the case of Vertex Cover, we describe a new approach to 2k kernelization based on iterative compression and crown reduction, providing a potentially useful alternative to the Nemhauser-Trotter 2k kernelization.
منابع مشابه
A Survey of FPT Algorithm Design Techniques with an Emphasis on Recent Advances and Connections to Practical Computing
The talk will survey the rich toolkit of FPT algorithm design methodologies that has developed over the last 20 years, including “older” techniques such as well-quasi-ordering, bounded treewidth, color-coding, reduction to a problem kernel, and bounded search trees — which have continued to deepen and advance — as well as some recently developed approaches such as win/win’s, greedy localization...
متن کاملAn Overview of Techniques for Designing Parameterized Algorithms
The field of parameterized algorithms continues to grow. It is a sign of its success that in the literature today there exists over 20 differently named techniques for designing parameterized algorithms. Many parameterized algorithms build on the same ideas, and as a problem solver it is important to be familiar with these general themes and ideas. Aside from several survey articles [6, 9], the...
متن کاملA kernel of order 2 k-c log k for vertex cover
In a recent paper Soleimanfallah and Yeo proposed a kernelization algorithm for Vertex Cover which, for any xed constant c, produces a kernel of order 2k−c in polynomial time. In this paper we show how their techniques can be extended to improve the produced kernel to order 2k − c log k, for any xed constant c.
متن کاملA Randomized Polynomial Kernelization for Vertex Cover with a Smaller Parameter
In the vertex cover problem we are given a graph G = (V,E) and an integer k and have to determine whether there is a set X ⊆ V of size at most k such that each edge in E has at least one endpoint in X. The problem can be easily solved in time O∗(2k), making it fixed-parameter tractable (FPT) with respect to k. While the fastest known algorithm takes only time O∗(1.2738k), much stronger improvem...
متن کاملIncompressibility through Colors and IDs
In parameterized complexity each problem instance comes with a parameter k, and a parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance to an instance with size polynomial in k. Many problems have been shown to admit polynomial kernels, but it is only recently that a framework for showing the non-existence of p...
متن کامل