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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Proceedings ArticleDOI
Parameterizing the Permanent: Genus, Apices, Minors, Evaluation Mod 2k
Radu Curticapean,Mingji Xia +1 more
TL;DR: Combined matchgates are used to prove the hardness of the permanent on k-apex graphs, implying its ⊕W[1]-hardness under the Hadwiger number, and a lower bound of nΩ(k/ log k) under the parity version of the exponential-time hypothesis is obtained.
Journal ArticleDOI
Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms
TL;DR: This paper improves the algorithmic analysis of both problems by proving a series of combinatorial results relating the branchwidth of planar graphs with their face cover by combining this fact with duality properties of branchwidth.
Proceedings ArticleDOI
Parameterized circuit complexity of model-checking on sparse structures
TL;DR: It is proved that for every class ℒ of graphs with effectively bounded expansion, given a first-order sentence φ and an n-element structure A, the question whether φ holds in A can be decided by a family of AC-circuits of size f and depth f.
Book ChapterDOI
On parameterized independent feedback vertex set
TL;DR: It is shown that IFVS can be solved in time O(5k nO(1) time where n is the number of vertices in the input graph G, and obtain a cubic O(k3) kernel for the problem.
Journal ArticleDOI
On the parameterized tractability of the just-in-time flow-shop scheduling problem
TL;DR: In this article, the authors study the parameterized complexity of a set of flow shop scheduling problems in which the objective is to maximize the weighted number of just-in-time jobs.