Plane digitization and related combinatorial problems

Some Combinatorial Problems in the Plane

1 Let there be given n points in the plane. Denote by t i the number of lines which contain exactly i of the points (2 < i < n). The properties of the set {ti } have been studied a great deal. For example, there is the classical result of Gallai and Sylvester : Assume to = 0 (i .e ., the points are not all on one line) ; then t2 > 0. For the history of this problem see, e.g ., Motzkin [6] and E...

Combinatorial and computational problems about points in the plane

We study three problems in combinatorial geometry. The problems investigated are con ict-free colorings of point sets in the plane with few colors, polychromatic colorings of the vertices of rectangular partitions in the plane and in higher dimensions and polygonalizations of point sets with few re ex points. These problems are problems of discrete point sets, the proofs are of combinatorial av...

Combinatorial problems related to origin-destination matrices

Combinatorial Objects in Bio-Algorithmics: Related problems and complexities

Unénorme mercì a celles qui font fonctionner le LIGM et l'IGM, avec qui les pauses cafés sont bien plus plaisantes. Mercì a mes co-auteurs qui ont indéniablement tous contribuéà monépanouissement scienti-fique. Mercì a Florian Sikora et Paul Morel d'avoir accepter d'ˆ etre mes doctorants cobayes. Finalement, un grand merci aux membres de ma famille età mes amis. Toutparticulì erement ma m` ere ...

Combinatorial Algorithms for Submodular Function Minimization and Related Problems

Submodular functions are common in combinatorics; examples include the cut capacity function of a graph and the rank function of a matroid. The submodular function minimization problem generalizes the classical minimum cut problem and also contains a number of other combinatorial optimization problems as special cases. In this thesis, we study submodular function minimization and two related pr...