Christophe Crespelle

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We present a fully dynamic algorithm that maintains three different representations of an interval graph: a minimal interval model of the graph, the PQ-tree of its maximal cliques, and its modular decomposition. After each vertex or edge modification (insertion or deletion), the algorithm determines whether the new graph is an interval graph in O(n) time,(More)
This paper presents an optimal fully-dynamic recognition algorithm for directed cographs. Given the modular decomposition tree of a directed cograph G, the algorithm supports arc and vertex modification (insertion or deletion) in O(d) time where d is the number of arcs involved in the operation. Moreover, if the modified graph remains a directed cograph,(More)
This paper considers the problem of maintaining a compact representation (O(n) space) of permutation graphs under vertex and edge modifications (insertion or deletion). That representation allows us to answer adjacency queries in O(1) time. The approach is based on a fully dynamic modular decomposition algorithm for permutation graphs that works in O(n)(More)
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs. However, this approach has, until now, severe limitations resulting from its incapacity to reproduce a key property of(More)
In this paper we address the problem of designing O(n) space representations for permutation and interval graphs that provide the neighborhood of any vertex in O(d) time, where d is its degree. To that purpose, we introduce a new parameter, called linearity, that would solve the problem if bounded for the two classes. Surprisingly, we show that it is not.(More)
In this paper, we design the first linear-time algorithm for computing the prime decomposition of a digraph G with regard to the cartesian product. A remarkable feature of our solution is that it computes the decomposition of G from the decomposition of its underlying undirected graph, for which there exists a linear-time algorithm. First, this allows our(More)
Many contributions use the degree distribution of IP-level internet topology. However, current knowledge of this property relies on biased and erroneous measurements, and so it is subject to much debate. We introduce here a new approach, dedicated to the core of the internet, which avoids the issues raised by classical measurements. It is based on the(More)
In this paper we show that the contiguity and linearity of cographs on n vertices are both O(log n). Moreover, we show that this bound is tight for contiguity as there exists a family of cographs on n vertices whose contiguity is Ω(log n). We also provide an Ω(log n/ log log n) lower bound on the maximum linearity of cographs on n vertices. As a by-product(More)
We present an O(n) Breadth-First Search algorithm for trapezoid graphs, which takes as input a trapezoid model and any priority order on the vertices. Our algorithm is the first able to produce any BFS-tree, and not only one specific to the model given as input, within this complexity. Moreover, it produces all the shortest paths from the root of the(More)