Parameterized algorithms of fundamental NP-hard problems: a survey

Parameterized computation theory has developed rapidly over the last two decades. In theoretical computer science, it has attracted considerable attention for its theoretical value and significant guidance in many practical applications. We give an overview on parameterized algorithms for some fundamental NP-hard problems, including MaxSAT, Maximum Internal Spanning Trees, Maximum Internal Out-Branching, Planar (Connected) Dominating Set, Feedback Vertex Set, Hyperplane Cover, Vertex Cover, Packing and Matching problems. All of these problems have been widely applied in various areas, such as Internet of Things, Wireless Sensor Networks, Artificial Intelligence, Bioinformatics, Big Data, and so on. In this paper, we are focused on the algorithms’ main idea and algorithmic techniques, and omit the details of them

A 13k-kernel for planar feedback vertex set via region decomposition

International audienc

Deep kernelization for the Tree Bisection and Reconnnect (TBR) distance in phylogenetics

We describe a kernel of size 9k-8 for the NP-hard problem of computing the Tree Bisection and Reconnect (TBR) distance k between two unrooted binary phylogenetic trees. We achieve this by extending the existing portfolio of reduction rules with three novel new reduction rules. Two of the rules are based on the idea of topologically transforming the trees in a distance-preserving way in order to guarantee execution of earlier reduction rules. The third rule extends the local neighbourhood approach introduced in (Kelk and Linz, Annals of Combinatorics 24(3), 2020) to more global structures, allowing new situations to be identified when deletion of a leaf definitely reduces the TBR distance by one. The bound on the kernel size is tight up to an additive term. Our results also apply to the equivalent problem of computing a Maximum Agreement Forest (MAF) between two unrooted binary phylogenetic trees. We anticipate that our results will be more widely applicable for computing agreement-forest based dissimilarity measures.Comment: 38 pages. In this version a figure has been added, some references have been added, some small typo's have been fixed and the introduction and conclusion have been slightly extended. Submitted for journal revie