Section: New Results
Graph and Combinatorial Algorithms
Collision-Free Network Exploration
In the collision-free exploration model considered
in [16] , a set of mobile agents is placed at different
nodes of a
In this work, we first considered the scenario when each mobile agent knows the
map of the network, as well as its own initial position. We established a
connection between the number of rounds required for collision-free exploration
and the degree of the minimum-degree spanning tree of the graph. We provided
tight (up to a constant factor) lower and upper bounds on the collision-free
exploration time in general graphs, and the exact value of this parameter for
trees. For our second scenario, in which the network is unknown to the agents,
we proposed collision-free exploration strategies running in
Properties of Graph Search Procedures
In [4] , we study the last vertex discovered by a graph search such as BFS or DFS. End-vertices of a given graph search may have some nice properties (as for example it is well known that the last vertex of Lexicographic Breadth First Search (LBFS) in a chordal graph is simplicial). Therefore it is interesting to consider if these vertices can be recognized in polynomial time or not. A graph search is a mechanism for systematically visiting the vertices of a graph. At each step of a graph search, the key point is the choice of the next vertex to be explored. Graph searches only differ by this selection mechanism during which a tie-break rule is used. In this paper we study how the choice of the tie-break rule can determine the complexity of the end-vertex problem for BFS or DFS. In particular we prove a counter-intuitive NP-completeness result for Breadth First Search, answering a question of D.G. Corneil, E. Köhler and J-M Lanlignel.
Matchings in Hypergraphs
A rainbow matching for (not necessarily distinct) sets
Common Intervals and Application to Genome Comparison
In [6] , we show how to identify generalized common and conserved nested intervals. This is a bio-informatics papers, explaining how to compute more relaxed variants of common or of conserved intervals of two permutations, which has applications in genome comparison. It also presents some properties of the family of intervals, useful for storing them.
Graph Decomposition
In [10] , we present a general framework for computing a large family of graph decomposition, the H-join. It generalizes some well know tools like modular decomposition or split decomposition. The paper explains how to compute it in polynomial time. A new canonical decomposition for sesquiprime graphs is also presented.
Combinatorial Optimization
Normal cone and subdifferential have been generalized through various continuous
functions; in [8] , we focus on a non separable