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
Fixed-parameter tractability and lower bounds for stabbing problems
TL;DR: It is shown that when S consists of axis-Parallel unit squares in R 2 the (decision) problem of stabbing S with axis-parallel lines is W[1]-hard with respect to k (and thus, not) the stabbing problem from a parameterized complexity point of view.
Book ChapterDOI
Exact Algorithms for the Max-Min Dispersion Problem.
Toshihiro Akagi,Tetsuya Araki,Takashi Horiyama,Shin-ichi Nakano,Yoshio Okamoto,Yota Otachi,Toshiki Saitoh,Ryuhei Uehara,Takeaki Uno,Kunihiro Wasa +9 more
TL;DR: The max-min k-dispersion problem can be solved in \(O(n^{\omega k/3} \log n)\) time and two special cases in which the problem can solve the problem quickly are shown.
Posted Content
Editing to a Graph of Given Degrees
TL;DR: An FPT-algorithm is constructed for Editing to a Graph of Given Degrees parameterized by d + k and it is shown that the problem has no polynomial kernel unless NP ?
Journal ArticleDOI
Parameterized Inapproximability of Target Set Selection and Generalizations
TL;DR: This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks and it is shown that for any functions f and $rho$ this problem cannot be approximated within a factor of $\rho(k)$ in f( k) \cdot n^{O(1)}$ time, unless FPT = W[P], even for restricted thresholds.
Journal ArticleDOI
The Constant Inapproximability of the Parameterized Dominating Set Problem
Yijia Chen,Bingkai Lin +1 more
TL;DR: A set $D$ of vertices of a graph G is a dominating set if every vertex of G is contained in D or adjacent to some vertex of D and the number of vertice in the smallest dominating set ofG is 1.