Andreas Brandstädt

Bipartite permutation graphs

This paper examines the class of bipartite permutation graphs. Two characterizations of graphs in this class are presented. These characterizations lead to a linear time recognition algorithm, and to polynomial time algorithms for a number of NP-complete problems when restricted to graphs in this class.

The NP-completeness of steiner tree and dominating set for chordal bipartite graphs

We show that the problems steiner tree, dominating set and connected dominating set are NP-complete for chordal bipartite graphs.

On domination problems for permutation and other graphs

Abstract There 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 ( n 2 ) for the weighted independent domination problem on permutation graphs (which is an improvement of the O ( n 3 ) 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.

On the restriction of some NP-complete graph problems to permutation graphs

Permutation graphs are known as a useful class of perfect graphs for which the NP-complete graph problems GRAPH k-COLORABILITY, PARTITION INTO CLIQUES, CLIQUE and INDEPENDENT SET (VERTEX COVER) (terminology from /8/) are solvable in polynomial time (/7/), in fact all four by the same algorithm (see /10/ for a presentation of these results).

Classes of bipartite graphs related to chordal graphs

Abstract This paper examines in a systematical way connections between chordal, strongly chordal and split graphs and bipartite graphs with chordality properties and introduces a further notion of chordality for bipartite graphs which is called here semichordality and which gives a natural extension of the class of chordal bipartite graphs and is incomparable with the class of perfect elimination bipartite graphs.

A relation between space, return and dual return complexities

Abstract We introduce the dual return complexity and prove that the return complexity classes and the dual return complexity classes of nondeterministic Turing machines coincide with the tape complexity classes of Turing machines with auxiliary pushdown tape for resource functions ƒ ⩾ id , id being the identity function.

The Jump Number Problem for Biconvex Graphs and Rectangle Covers of Rectangular Regions

Let P=(V, ≤p) be a finite partially ordered set (poset) with |V|=n and let L=(1l,...,1n) be a linear extension of P. The pair (1i,1i+1), 1≤i≤n-1, is a jump of P in L if n n. The jump number problem is the problem of finding the minimum number of jumps in any linear extension of a given poset P. It is known that for posets P1,P2 with the same comparability graph also the jump numbers of P1 and P2 coincide and that for chordal bipartite graphs the jump number decision problem is NP-complete.

Uniform simulations of nondeterministic real time multitape turing machines

A new and uniform technique is developed for the simulation of nondeterministic multitape Turing machines by simpler machines. For many types of restricted nondeterministic Turing machines it can now be proved that both linear time is no more powerful than real time, and multitape machines are no more powerful than machines with two tapes, one of which is a simple and normalized comparison tape. This is an improvement over all previously known simulations in terms of weaker machines. As an application we obtain that, for all such machines, the class of languages accepted in real time by multitape machines is principal and has a simple trio generator. Moreover, multitape machines with different types of tapes are hierarchically related, contrasting with the case of one-tape machines, and some important families of languages are characterized in a new way.

Reversal-Bounded and Visit-Bounded Realtime Computations

First it is dealt with the class RBQ (also sometimes called BNP) of all languages acceptable in linear time by reversal-bounded nondeterministic multitape Turing machines.