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
Augmenting Graphs to Minimize the Diameter
TL;DR: In this article, the authors study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph, and present an FPT $$4$$4-approximation algorithm.
Journal ArticleDOI
Voting and Bribing in Single-Exponential Time
TL;DR: It is shown that R-Multi-Bribery is fixed-parameter tractable parameterized by the number of candidates for many natural voting rules R, including Kemeny rule, all scoring protocols, maximin rule, Bucklin rule, fallback rule, SP-AV, and any C1 rule.
Journal ArticleDOI
The Linear Arrangement Problem Parameterized Above Guaranteed Value
TL;DR: An algorithm is derived which decides in time O(m + n + 5.88k) whether a given graph with m edges and n vertices admits an LA of cost at most m + k (the algorithm computes such an LA if it exists), based on a procedure which generates a problem kernel of linear size in linear time for a connected graph G.
Proceedings ArticleDOI
On the Parameterized and Approximation Hardness of Metric Dimension
Sepp Hartung,André Nichterlein +1 more
TL;DR: In this paper, a polynomial-time reduction from the Bipartite Dominating Set problem to metric dimension on maximum degree three graphs was shown. But this reduction requires the assumption that FPT≠W[1] fails.
Posted Content
Fair Knapsack
TL;DR: Three approaches to aggregating voters' preferences are studied, motivated by the literature on multiwinner elections and fair allocation, and the concepts of individually best, diverse, and fair knapsack are introduced.