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
The parameterized complexity of editing graphs for bounded degeneracy
TL;DR: The parameterized complexity of the problem of editing a graph to obtain an r-degenerate graph is examined, and it is shown that for the editing operations vertex deletion and edge deletion, the problem is W[P]-complete, and remains W-complete even if the input graph is already (r+1)-degenerated.
Book ChapterDOI
Constrained Swap Dynamics over a Social Network in Distributed Resource Reallocation
TL;DR: A resource allocation problem where each agent is to be assigned exactly one object and questions are investigated through parameterized complexity, focusing on budget constraints such as the number of exchanges an agent may be involved in or the total duration of the process.
Journal ArticleDOI
Parameterized Algorithms for Finding Square Roots
TL;DR: The first result implies that squares of graphs obtained from trees by adding at most $$k$$k edges can be recognized in polynomial time for every fixed $$k\ge 0$$k≥0; previously this result was known only for $$k=0$$ k=0.
Book ChapterDOI
Efficient enumeration for conjunctive queries over x-underbar structures
TL;DR: It is shown that query evaluation is NP-hard and, unless P = NP, these queries do not admit enumeration algorithms with a combined polynomial time delay, but it is also shown that hardness relies only on the number l of variables that appear in inequalities.
Journal ArticleDOI
Hull number: P5-free graphs and reduction rules
Júlio Araújo,Júlio Araújo,Grégory Morel,Leonardo Sampaio,Ronan Pardo Soares,Ronan Pardo Soares,Valentin Weber +6 more
TL;DR: A fixed parameter tractable algorithm is proposed to compute the hull number of any graph G, where the parameter can be the size of a vertex cover of G or, more generally, its neighborhood diversity, and four reduction rules are presented based on vertices with the same neighborhood.