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
Maximum balanced subgraph problem parameterized above lower bound
TL;DR: In this paper, the authors considered the problem of finding a balanced subgraph with at least m 2+n-14+k4 edges, where k is the parameter, and obtained an algorithm for the problem in polynomial time.
DissertationDOI
Fixed-Parameter Linear-Time Algorithms for NP-hard Graph and Hypergraph Problems Arising in Industrial Applications
TL;DR: This thesis aims for the development of efficient algorithms to exactly solve four selected NPhard graph and hypergraph problems arising in the fields of scheduling, steel manufacturing, software engineering, radio frequency allocation, computer-aided circuit design and social network analysis.
Journal ArticleDOI
Confronting intractability via parameters
TL;DR: The theory of computational complexity has been widely used in a number of areas of applications including computational biology, linguistics, VLSI design, learning theory and many others as mentioned in this paper.
Journal ArticleDOI
Graphs with few P 4 's under the convexity of paths of order three
TL;DR: It is proved that the Caratheodory number is at most three for every cograph, P 4 -sparse graph and every connected ( q, q - 4 ) -graph with at least q vertices.
Posted Content
Win-Win Kernelization for Degree Sequence Completion Problems
TL;DR: This work shows fixed-parameter tractability for NP-hard graph completion (that is, edge addition) cases while it shows that there is no hope to achieve analogous results for the corresponding vertex or edge deletion versions.