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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Kernel(s) for Problems With no Kernel: On Out-Trees With Many Leaves
TL;DR: This work gives the first polynomial kernel for Rooted k-Leaf-Out-Branching, a variant of k- leaf- out-branching where the root of the tree searched for is also a part of the input, and is the first ones separating Karp kernelization from Turing kernelization.
Journal ArticleDOI
There is no EPTAS for two-dimensional knapsack
Ariel Kulik,Hadas Shachnai +1 more
TL;DR: There is no EPTAS for d-dimensional knapsack, already for d=2, unless W[1]=FPT, and it is shown that unless all problems in SNP are solvable in sub-exponential time, there is no approximation scheme for two-dimensionalknapsack whose running time is f(1/@e)|I|^o^(^1^/^@e^), for any function f.
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Testing first-order properties for subclasses of sparse graphs
TL;DR: In this article, a linear-time algorithm for determining first-order (FO) properties in classes of graphs with bounded expansion, a notion recently introduced by Nesetril and Ossona de Mendez, is presented.
Book ChapterDOI
Parameterized Algorithms for Modular-Width
TL;DR: It is argued that modular-width occupies a sweet spot as a graph parameter, generalizing several simpler notions on dense graphs but still evading the "price of generality" paid by clique-width.
Journal ArticleDOI
Efficient Exact Algorithms through Enumerating Maximal Independent Sets and Other Techniques
TL;DR: The algorithms that are presented are the best known and are a substantial improvement over previous best results.