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We provide an algorithm listing all minimal dominating sets of a graph on <i>n</i> vertices in time <i>O</i>(1.7159<sup><i>n</i></sup>). This result can be seen as an algorithmic proof of the fact that the number of minimal dominating sets in a graph on <i>n</i> vertices is at most 1.7159<sup><i>n</i></sup>, thus improving on the trivial… (More)

Branch & Reduce and dynamic programming on graphs of bounded treewidth are among the most common and powerful techniques used in the design of moderately exponential time exact algorithms for NP hard problems. In this paper we discuss the efficiency of simple algorithms based on combinations of these techniques. The idea behind these algorithms is very… (More)

We show that the number of minimal dominating sets in a graph on n vertices is at most 1.7697 n , thus improving on the trivial O(2 n / √ n) bound. Our result makes use of the measure and conquer technique from exact algorithms, and can be easily turned into an O(1.7697 n) listing algorithm. Based on this result, we derive an O(2.8805 n) algorithm for the… (More)

- Frederic Dorn, Joanna Bauer, Lene Favrholdt, Serge Gaspers, Petr Golovach, Pinar Heggernes +16 others
- 2007

In this thesis we focus on subexponential algorithms for NP-hard graph problems: exact and parameterized algorithms that have a truly subexponential running time behavior. For input instances of size n we study exact algorithms with running time 2 O(√ n) and parameterized algorithms with running time 2 O(√ k) ·n O(1) with parameter k, respectively. We study… (More)

We consider the well studied Full Degree Spanning Tree problem, a NP-complete variant of the Spanning Tree problem, in the realm of moderately exponential time exact algorithms. In this problem , given a graph G, the objective is to find a spanning tree T of G which maximizes the number of vertices that have the same degree in T as in G. This problem is… (More)

We show how to count all minimum weighted dominating sets of a graph on n vertices in time O(1.5535 n).

We are considering the N P-hard problem of finding a spanning tree with many internal vertices. This problem is a generalization of the famous and well-studied Hamiltonian Path problem. We present an dynamic-programming approach for general and degree-bounded graphs obtaining a run times of the form O * (c n) (c ≤ 3). The main result is an algorithm for the… (More)

We introduce a surprisingly simple technique to design and analyze algorithms based on search trees, that significantly improves many existing results in the area of exact algorithms. The technique is based on measuring the progress of Branch & Bound algorithms by making use of a combinatorial relation between the average and maximum dual degrees of a… (More)

Branch & Reduce and dynamic programming on graphs of bounded treewidth are among the most common and powerful techniques used in the design of moderately exponential time exact algorithms for NP hard problems. In this paper we discuss the efficiency of simple algorithms based on combinations of these techniques. The idea behind these algorithms is very… (More)