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
Searching the k-change neighborhood for TSP is W[1]-hard
TL;DR: It is shown that searching the k-change neighborhood is W[1]-hard for metric TSP, which means that finding the best tour in the k -change neighborhood essentially requires complete search (modulo some complexity-theoretic assumptions).
Posted Content
Contracting Graphs to Paths and Trees
TL;DR: It is shown that Path Contraction has a kernel with at most 5k+3 vertices, while Tree Contraction does not have a polynomial kernel unless NP ⊆ coNP/poly, which is surprising.
Journal ArticleDOI
Causal graphs and structurally restricted planning
Hubie Chen,Omer Giménez +1 more
TL;DR: In this article, the complexity of planning restricted by the causal graph is studied, and it is shown that a set of causal graphs is either polynomial-time tractable or not tractable unless an established complexity-theoretic assumption fails.
Journal ArticleDOI
Kernel(s) for problems with no kernel: On out-trees with many leaves
Daniel Binkele-Raible,Henning Fernau,Fedor V. Fomin,Daniel Lokshtanov,Saket Saurabh,Yngve Villanger +5 more
TL;DR: For the k-Leaf-Out-Branching problem, it was shown in this paper that no polynomial-sized kernel is possible unless coNP is in NP/poly.
Proceedings ArticleDOI
Beyond worst-case analysis for joins with minesweeper
TL;DR: In this paper, a new algorithm, Minesweeper, was proposed that is able to satisfy stronger runtime guarantees than previous join algorithms for data in indexed search trees, which is referred to as certificate complexity.