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This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
Parameterized graph separation problems
- D. Marx
- MathematicsTheor. Comput. Sci.
- 14 September 2004
Size Bounds and Query Plans for Relational Joins
- Albert Atserias, Martin Grohe, D. Marx
- Computer Science49th Annual IEEE Symposium on Foundations of…
- 25 October 2008
This work studies relational joins from a theoretical perspective and shows that there exist queries for which the join-project plan suggested by the fractional edge cover approach may be substantially better than any join plan that does not use intermediate projections.
Parameterized Complexity and Approximation Algorithms
- D. Marx
- Computer ScienceComput. J.
The different ways parameterized complexity can be extended to approximation algorithms, survey results of this type and proposed directions for future research are discussed.
Fixed-parameter tractability of multicut parameterized by the size of the cutset
It is unlikely that an algorithm with running time of the form f(p) ⋅ n<sup>O(1)</sup> exists for the directed version of the problem, as it is shown to be W-hard parameterized by the size of the cutset.
Lower bounds based on the Exponential Time Hypothesis
This chapter proves lower bounds based on ETH for the time needed to solve various problems, and in many cases these lower bounds match the running time of the best known algorithms for the problem.
Constraint solving via fractional edge covers
It is proved that constraint satisfaction problems with bounded fractional hypertree width can be solved in polynomial time (provided that a the tree decomposition is given in the input) and that certain parameterized constraint satisfaction, homomorphism, and embedding problems are fixed-parameter tractable on instances having bounded fractionsalhypertree width.
Known algorithms on graphs of bounded treewidth are probably optimal
Lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth are obtained and the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi are proved.
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
- D. Marx
- Computer Science, MathematicsJACM
- 4 November 2009
The goal is to characterize those classes of hypergraphs for which CSP(H) is polynomial-time solvable or fixed-parameter tractable, parameterized by the number of variables, and to prove via a series of combinatorial results that if a hypergraph H has large submodular width, then a 3SAT instance can be efficiently simulated by a CSP instance whose hypergraph is H.