Mathieu Liedloff
University of Orléans
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Publication
Featured researches published by Mathieu Liedloff.
Algorithmica | 2012
Serge Gaspers; Dieter Kratsch; Mathieu Liedloff
Bicliques of graphs have been studied extensively, partially motivated by the large number of applications. In this paper we improve Prisner’s upper bound on the number of maximal bicliques (Combinatorica, 20, 109–117, 2000) and show that the maximum number of maximal bicliques in a graph on n vertices is Θ(3n/3). Our major contribution is an exact exponential-time algorithm. This branching algorithm computes the number of distinct maximal independent sets in a graph in time O(1.3642n), where n is the number of vertices of the input graph. We use this counting algorithm and previously known algorithms for various other problems related to independent sets to derive algorithms for problems related to bicliques via polynomial-time reductions.
Theoretical Computer Science | 2011
Henning Fernau; Joachim Kneis; Dieter Kratsch; Alexander Langer; Mathieu Liedloff; Daniel Raible; Peter Rossmanith
Given an undirected graph with n vertices, the Maximum Leaf Spanning Tree problem is to find a spanning tree with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4kpoly(n)) using a simple branching algorithm introduced by a subset of the authors (Kneis et al. 2008 16). Daligault et al. (2010) 6 improved the branching and obtained a running time of O(3.72kpoly(n)). In this paper, we study the problem from an exponential time viewpoint, where it is equivalent to the Connected Dominating Set problem. Here, Fomin, Grandoni, and Kratsch showed how to break the ?(2n) barrier and proposed an O(1.9407n)-time algorithm (Fomin et al. 2008 11). Based on some useful properties of Kneis et al. (2008) 16 and Daligault et al. (2010) 6, we present a branching algorithm whose running time of O(1.8966n) has been analyzed using the Measure-and-Conquer technique. Finally, we provide a lower bound of ?(1.4422n) for the worst case running time of our algorithm.
Algorithmica | 2013
Daniel Binkele-Raible; Henning Fernau; Serge Gaspers; Mathieu Liedloff
We consider the
Algorithmica | 2011
Frédéric Havet; Martin Klazar; Jan Kratochvíl; Dieter Kratsch; Mathieu Liedloff
\mathcal{NP}
mathematical foundations of computer science | 2008
Fedor V. Fomin; Serge Gaspers; Dieter Kratsch; Mathieu Liedloff; Saket Saurabh
-hard problem of finding a spanning tree with a maximum number of internal vertices. This problem is a generalization of the famous Hamiltonian Path problem. Our dynamic-programming algorithms for general and degree-bounded graphs have running times of the form
Journal of Discrete Algorithms | 2011
Daniel Binkele-Raible; Marek Cygan; Henning Fernau; Joachim Kneis; Dieter Kratsch; Alexander Langer; Mathieu Liedloff; Marcin Pilipczuk; Peter Rossmanith; Jakub Onufry Wojtaszczyk
\mathcal{O}^{*}(c^{n})
Parameterized and Exact Computation | 2009
Henning Fernau; Joachim Kneis; Dieter Kratsch; Alexander Langer; Mathieu Liedloff; Daniel Raible; Peter Rossmanith
with c≤2. For graphs with bounded degree, c<2. The main result, however, is a branching algorithm for graphs with maximum degree three. It only needs polynomial space and has a running time of
mathematical foundations of computer science | 2007
Jan Kratochvíl; Dieter Kratsch; Mathieu Liedloff
\mathcal{O}(1.8612^{n})
workshop on graph theoretic concepts in computer science | 2005
Mathieu Liedloff; Ton Kloks; Jiping Liu; Sheng-Lung Peng
when analyzed with respect to the number of vertices. We also show that its running time is
Theoretical Computer Science | 2015
Jean-François Couturier; Romain Letourneur; Mathieu Liedloff
2.1364^{k} n^{\mathcal{O}(1)}