• Publications
  • Influence
A survey of the algorithmic aspects of modular decomposition
  • M. Habib, C. Paul
  • Mathematics, Computer Science
  • Comput. Sci. Rev.
  • 8 December 2009
TLDR
Modular decomposition is a technique at the crossroads of several domains of combinatorics which applies to many discrete structures such as graphs, 2-structures, hypergraphs. Expand
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Approximate Distance Labeling Schemes
  • C. Gavoille, C. Paul
  • Mathematics, Computer Science
  • Electron. Notes Discret. Math.
  • 1 July 2000
TLDR
We show how to label the nodes of every interval graphs of diameter D with integers of size [log- D ] + 1 bits so that the distance up to an additive factor 1 between two distinct nodes can be computed in constant time from their labels only. Expand
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Split decomposition and graph-labelled trees: characterizations and fully-dynamic algorithms for totally decomposable graphs
  • E. Gioan, C. Paul
  • Computer Science, Mathematics
  • Discret. Appl. Math.
  • 10 October 2008
TLDR
We revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses, namely the cographs and the 3-leaf power graphs. Expand
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Fully-Dynamic Recognition Algorithm and Certificate for Directed Cographs
TLDR
This paper presents an optimal fully-dynamic recognition algorithm for directed cographs. Expand
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Eclecticism shrinks even small worlds
TLDR
We consider small world graphs as defined by Kleinberg (2000), i.e., graphs obtained from a d-dimensional augmented meshes by adding links chosen at random according to the d-harmonic distribution. Expand
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Quartets and Unrooted phylogenetic Networks
TLDR
In this article, we link abstract and explicit networks through their combinatorial properties, by introducing the unrooted analog of level-k networks. Expand
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Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing
TLDR
We give a O(n+mlogn) algorithm for transitive orientation of a comparability graph, and simple linear algorithms to recognize interval graphs, convex graphs, Y-semichordal graphs and matrices that have consecutive ones property. Expand
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A simple linear time algorithm for cograph recognition
  • M. Habib, C. Paul
  • Computer Science, Mathematics
  • Discret. Appl. Math.
  • 15 January 2005
TLDR
In this paper, we describe a new simple linear time algorithm to recognize cographs. Expand
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Interval Completion Is Fixed Parameter Tractable
TLDR
We present an algorithm with runtime $O(k^{2k}n^3m) for the k-Interval Completion problem of deciding whether a graph on n vertices and m edges can be made into an interval graph by adding at most k edges. Expand
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Perfect Sorting by Reversals Is Not Always Difficult
TLDR
We characterize a class of signed permutations for which one can compute in polynomial time a reversal scenario that conserves all common intervals, and that is parsimonious among such scenarios. Expand
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