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Journals and Conferences
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 treedecomposition 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.
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 kPath, k-Cycle, k-Exact Cycle,… (More)
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.
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)
A short overview is given of many recent results in algorithmic graph theory that deal with the notions treewidth, and pathwidth. We discuss algorithms that nd tree-decompositions, algorithms that use tree-decompositions to solve hard problems eeciently, graph minor theory, and some applications. The paper contains an extensive bibliography.
In this paper we give, for all constants k, l, explicit algorithms that, given a graph Ž . G s V, E with a tree-decomposition of G with treewidth at most l, decide Ž . whether the treewidth or pathwidth of G is at most k, and, if so, find a Ž . tree-decomposition or path-decomposition of G of width at most k, and that use Ž < <. O V time. In contrast with… (More)
This paper gives an overview of several results and techniques for graphs algorithms that compute the treewidth of a graph or that solve otherwise intractable problems when restricted graphs with bounded treewidth more e ciently. Also, several results on graph minors are reviewed.
One of the major efforts in molecular biology is the computation of phylogenies for species sets. A longstanding open problem in this area is called the Perfect Phylogeny problem. For almost two decades the complexity of this problem remained open, with progress limited to polynomial time algorithms for a few special cases, and many relaxations of the… (More)
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)
In a parameterized problem, every instance <i>I</i> comes with a positive integer <i>k</i>. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance <i>I</i> to a polynomial in <i>k</i> while preserving the answer. In this work, we give two meta-theorems on kernelization. The first theorem says that… (More)