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- Hans L. Bodlaender
- STOC
- 1993

In this paper, we give, for constant k, a linear time algorithm , that given a graph G = (V, E), determines whether the treewidth of G is at most k, and if so, finds a tree-decomposition of G with treewidth at most k. A consequence is that every minor-closed class of graphs that does not contain all planar graphs has a linear time recognition algorithm.

- Hans L. Bodlaender, Rodney G. Downey, Michael R. Fellows, Danny Hermelin
- J. Comput. Syst. Sci.
- 2009

Kernelization is a central technique used in parameterized algorithms, and in other techniques for coping with NP-hard problems. In this paper, we introduce a new method which allows us to show that many problems do not have polynomial size kernels under reasonable complexity-theoretic assumptions. These problems include k

- Jochen Alber, Hans L. Bodlaender, Henning Fernau, Ton Kloks, Rolf Niedermeier
- Algorithmica
- 2002

Abstract. We present an algorithm that constructively produces a solution to the k -DOMINATING SET problem for planar graphs in time O(c^ \sqrt k n) , where c=4^ 6\sqrt 34 . To obtain this result, we show that the treewidth of a planar graph with domination number γ (G) is O(\sqrt \rule 0pt 4pt \smash γ (G) ) , and that such a tree decomposition can be… (More)

- Hans L. Bodlaender
- Theor. Comput. Sci.
- 1998

The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between such classes are discussed.

- Hans L. Bodlaender, Stéphan Thomassé, Anders Yeo
- ESA
- 2009

In this paper, we give evidence for the problems Disjoint Cycles and Disjoint Paths that they cannot be preprocessed in polynomial time such that resulting instances always have a size bounded by a polynomial in a specified parameter (or, in short: do not have a polynomial kernel); these results are assuming the validity of certain complexity theoretic… (More)

- Irit Katriel, Hans L. Bodlaender
- SODA
- 2005

It is shown that the problem of maintaining the topological order of the nodes of a directed acyclic graph while inserting <i>m</i> edges can be solved in <i>O</i>(min{<i>m</i><sup>3/2 log <i>n m</i>3/3</sup> + <i>n</i><sup>2</sup> log <i>n</i>}) time, an improvement over the best known result of <i>O</i>(<i>mn</i>). In addition, we analyze the complexity… (More)

- Hans L. Bodlaender
- SWAT
- 1988

- Hans L. Bodlaender, Michael R. Fellows, Tandy J. Warnow
- ICALP
- 1992

- Hans L. Bodlaender, Arie M. C. A. Koster
- Comput. J.
- 2008

There are many graph problems that can be solved in linear or polynomial time with a dynamic programming algorithm when the input graph has bounded treewidth. For combinatorial optimization problems, this is a useful approach for obtaining fixed-parameter tractable algorithms. Starting from trees and series-parallel graphs, we introduce the concepts of… (More)

- Hans L. Bodlaender, Bart M. P. Jansen, Stefan Kratsch
- SIAM J. Discrete Math.
- 2014

We introduce the cross-composition framework for proving kernelization lower bounds. A classical problem L and/or-cross-composes into a parameterized problem Q if it is possible to efficiently construct an instance of Q with polynomially bounded parameter value that expresses the logical and or or of a sequence of instances of L. Building on work by… (More)