We consider here a NP-hard problem related to the Routing and Wavelength Assignment (RWA) problem in optical networks, dealing with Scheduled Lightpath Demands (SLDs). An SLD is a connection demand between two nodes of the network, during a certain time. Given a set of SLDs, we want to assign a...

In this paper, we study a method of classification by density in an unweighted graph. We search some areas with a high density of edges, that can be overlapping (we don't try to obtain a partition but some intrinsic classes). The method consists of two steps ; first we determine the cores of the...

Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T; a Copeland winner of T is a vertex with a maximum out-degree. In this paper, we show that 13 is the minimum number of vertices that a tournament must have so...

This paper presents the -linked- notions of metric and latticial medians and it explains what is the median procedure for the consensus problems, in particular in the case of the aggregation of linear orders. First we consider the medians of a v-tuple of arbitrary or particular binary...

Given a finite set X and a collection Π, called a profile, of binary relations defined on X (which can be linear orders, complete preorders, any relations, and so on), a relation R is said to be median if it minimizes the total number of disagreements with respect to Π. In the context of...

Given a tournament T, Slater's problem consists in determining a linear order (i.e. a complete directed graph without directed cycles) at minimum distance from T, the distance between T and a linear order O being the number of directed edges with different orientations in T and in O. This paper...

Given a tournament T, a Banks winner of T is the first vertex of any maximal (with respect to inclusion) transitive subtournament of T. While Woeginger shows that recognizing whether a given vertex of T is a Banks winner is NP-complete, the computation of a Banks winner of T is polynomial, and...