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
Citations
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Journal ArticleDOI
Linear Time Algorithms for Finding a Dominating Set of Fixed Size in Degenerated Graphs
Noga Alon,Shai Gutner +1 more
TL;DR: This paper gives a kO(dk)n time algorithm for finding a dominating set of size at most k in a d-degenerated graph with n vertices, which proves that the dominating set problem is fixed-parameter tractable for degenerated graphs.
Journal ArticleDOI
Parameterized Complexity of Cardinality Constrained Optimization Problems
TL;DR: This work obtains faster exact algorithms for several cardinality constrained optimization problems by transforming them into problems of finding maximum (minimum) weight triangles in weighted graphs.
Book ChapterDOI
Fast FAST
TL;DR: This work presents a randomized subexponential time, polynomial space parameterized algorithm for the k -Weighted Feedback Arc Set in Tournaments (k -FAST ) problem and is the first non-trivial subexp exponential time parameterized algorithms outside the framework of bidimensionality.
Journal ArticleDOI
Short Cycles Make W -hard Problems Hard: FPT Algorithms for W -hard Problems in Graphs with no Short Cycles
Venkatesh Raman,Saket Saurabh +1 more
TL;DR: It is shown that several problems that are hard for various parameterized complexity classes on general graphs, become fixed parameter tractable on graphs with no small cycles.
Proceedings ArticleDOI
A quadratic kernel for feedback vertex set
TL;DR: It is proved that given an undirected graph G on n vertices and an integer k, one can compute in polynomial time in n a graph G' such that G has a feedback vertex set of size at most k iff G' has a Feedback vertices set ofsize at mostk'.