Open AccessBook
Parameterized complexity theory
Jörg Flum,Martin Grohe +1 more
TLDR
Fixed-Parameter Tractability.Abstract:
Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- The W-Hierarchy.- The A- Hierarchy.- Kernelization and Linear Programming Techniques.- The Automata-Theoretic Approach.- Tree Width.- Planarity and Bounded Local Tree Width.- Homomorphisms and Embeddings.- Parameterized Counting Problems.- Bounded Fixed-Parameter Tractability.- Subexponential Fixed-Parameter Tractability.- Appendix, Background from Complexity Theory.- References.- Notation.- Index.read more
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Journal ArticleDOI
Parameterized complexity of k-Chinese Postman Problem
TL;DR: In this paper, it was shown that the k-Chinese postman problem is fixed-parameter tractable when parameterized by k. In fact, the problem admits a kernel with O(k^2logk) vertices.
Proceedings ArticleDOI
Counting crossing-free structures
TL;DR: This paper develops a general technique for computing the number of crossing-free structures of an input set P and shows that the techniques are general enough to solve the restricted triangulation counting problem, which is proved to be W[2]-hard in the parameter k.
Proceedings Article
Variable-deletion backdoors to planning
TL;DR: This work defines a new type of variable-deletion backdoors based on the extended causal graph of a planning instance, which explores the capabilities of polynomial time preprocessing and shows the close connection between planning and verification problems such as Vector Addition System with States (VASS).
Posted Content
Constructing minimal phylogenetic networks from softwired clusters is fixed parameter tractable
Steven Kelk,Celine Scornavacca +1 more
TL;DR: In this article, it was shown that given a set of clusters C on a taxa X, where |X|=n, it is possible to determine in time f(k).poly(n) whether there exists a level-<-k network (i.e., a network where each biconnected component has reticulation number at most k) that represents all the clusters in C in the softwired sense, and if so to construct such a network.
Proceedings ArticleDOI
The Complexity of Ontology-Based Data Access with OWL 2 QL and Bounded Treewidth Queries
Meghyn Bienvenu,Stanislav Kikot,Roman Kontchakov,Vladimir V. Podolskii,Vladislav Ryzhikov,Michael Zakharyaschev +5 more
TL;DR: It is shown that OMQs with bounded depth ontologies have nonrecursive datalog (NDL) rewritings that can be constructed and evaluated in LOGCFL for combined complexity, and even in NL if their CQs are tree-shaped with a bounded number of leaves.