Irène Charon

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Consider a connected undirected graph G = (V, E), a subset of vertices C ⊆ V , and an integer r ≥ 1; for any vertex v ∈ V , let Br (v) denote the ball of radius r centered at v, i.e., the set of all vertices within distance r from v. If for all vertices v ∈ V (respectively, v ∈ V \C), the sets Br (v) ∩ C are all nonempty and different, then we call C an r(More)
Let G = (V,E) be a connected undirected graph and S a subset of vertices. If for all vertices v ∈ V , the sets Br(v) ∩ S are all nonempty and different, where Br(v) denotes the set of all points within distance r from v, then we call S an r-identifying code. We give constructive upper bounds on the best possible density of r-identifying codes in four(More)
Consider a connected undirected graph G = (V,E) and a subset of vertices C. If for all vertices v ∈ V , the sets Br(v) ∩ C are all nonempty and pairwise distinct, where Br(v) denotes the set of all points within distance r from v, then we call C an r-identifying code. We give general lower and upper bounds on the best possible density of r-identifying codes(More)
In this paper, we survey some results, conjectures and open problems dealing with the combinatorial and algorithmic aspects of the linear ordering problem. This problem consists in finding a linear order which is at minimum distance from a (weighted or not) tournament. We show how it can be used to model an aggregation problem consisting of going from(More)
The linear ordering problem consists in finding a linear order at minimum remoteness from a weighted tournament T, the remoteness being the sum of the weights of the arcs that we must reverse in T to transform it into a linear order. This problem, also known as the search of a median order, or of a maximum acyclic subdigraph, or of a maximum consistent set,(More)