Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs

We present space-efficient algorithms for computing cut vertices in a given graph with $n$ vertices and $m$ edges in linear time using $O(n+\min\{m,n\log \log n\})$ bits. With the same time and using $O(n+m)$ bits, we can compute the biconnected components of a graph. We use this result to show an algorithm for the recognition of (maximal) outerplanar graphs in $O(n\log \log n)$ time using $O(n)$ bits

On claw-free asteroidal triple-free graphs

AbstractWe present an O(n2.376) algorithm for recognizing claw-free AT-free graphs and a linear-time algorithm for computing the set of all central vertices of a claw-free AT-free graph. In addition, we give efficient algorithms that solve the problems INDEPENDENT SET, DOMINATING SET, and COLORING. We argue that all running times achieved are optimal unless better algorithms for a number of famous graph problems such as triangle recognition and bipartite matching have been found. Our algorithms exploit the structure of 2LexBFS schemes of claw-free AT-free graphs

On domination problems for permutation and other graphs

AbstractThere is an increasing interest in results on the influence of restricting NP-complete graph problems to special classes of perfect graphs as, e.g., permutation graphs. It was shown that several problems restricted to permutation graphs are solvable in polynomial time [2, 3, 4, 6, 7, 14, 16].In this paper we give 1.(i) an algorithm with time bound O(n2) for the weighted independent domination problem on permutation graphs (which is an improvement of the O(n3) solution given in [7]);2.(ii) a polynomial time solution for the weighted feedback vertex set problem on permutation graphs;3.(iii) an investigation of (weighted) dominating clique problems for several graph classes including an NP-completeness result for weakly triangulated graphs as well as polynomial time bounds

Tree-visibility orders

AbstractWe introduce a new class of partially ordered sets, called tree-visibility orders, containing interval orders, duals of generalized interval orders and height one orders. We give a characterization of tree-visibility orders by an infinite family of minimal forbidden suborders. Furthermore, we present an efficient recognition algorithm for tree-visibility orders

Measuring the vulnerability for classes of intersection graphs

AbstractA general method for the computation of various parameters measuring the vulnerability of a graph is introduced. Four measures of vulnerability are considered, i.e., the toughness, scattering number, vertex integrity and the size of a minimum balanced separator. We show how to compute these parameters by polynomial-time algorithms for various classes of intersection graphs like permutation graphs, bounded dimensional cocomparability graphs, interval graphs, trapezoid graphs and circular versions of these graph classes

On treewidth and minimum fill-in of asteroidal triple-free graphs

We present O(n5R + n3R3) time algorithms to compute the treewidth, pathwidth, minimum fill-in and minimum interval graph completion of asteroidal triple-free graphs, where n is the number of vertices and R is the number of minimal separators of the input graph. This yields polynomial time algorithms for the four NP-complete graph problems on any subclass of the asteroidal triple-free graphs that has a polynomially bounded number of minimal separators, as e.g. cocomparability graphs of bounded dimension and d-trapezoid graphs for any fixed d ⩾ 1

08431 Abstracts Collection -- Moderately Exponential Time Algorithms

From $19/10/2008$ to $24/10/2008$, the Dagstuhl Seminar 08431 ``Moderately Exponential Time Algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available