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This thesis is concerned with computations of bounds for two different arithmetic invariants. In both cases it is done with the intention of proving some algebraic or arithmetic properties for number fields. The first part is devoted to computations of low ...
A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are mini ...
Holt and Klee have recently shown that every (generic) LP orientation of the graph of a d-polytope satisfies a directed version of the d-connectivity property, i.e. there are d internally disjoint directed paths from a unique source to a unique sink. We in ...
Computing the weighted coloring number of graphs is a classical topic in combinatorics and graph theory. Recently these problems have again attracted a lot of attention for the class of quasi-line graphs and more specifically fuzzy circular interval graphs ...
A new region-based depth ordering algorithm is proposed based on the segmented motion layers with affine motion models. Starting from an initial set of layers that are independently extracted for each frame of an input sequence, relative depth order of eve ...
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Formation building and keeping among vehicles has been studied for many years, since 1987 with Reynold's rules. This paper presents a control algorithm, based on recent work in graph theory, able to reconfigure static formations of non-holonomic vehicles e ...
A linear compressive network (LCN) is defined as a graph of sensors in which each encoding sensor compresses incoming jointly Gaussian random signals and transmits (potentially) low-dimensional linear projections to neighbors over a noisy uncoded channel. ...
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Pervasive communications bring along new privacy challenges, fueled by the capability of mobile devices to communicate with, and thus "sniff on", each other directly. We design a new mechanism that aims at achieving location privacy in these forthcoming mo ...
The fundamentals of interval analysis on directed acyclic graphs (DAGs) for global optimization and constraint propagation have recently been proposed in Schichl and Neumaier (J. Global Optim. 33, 541-562, 2005). For representing numerical problems, the au ...
Starting from the basic problem of reconstructing a 2-dimensional image given by its projections on two axes, one associates a model of edge coloring in a complete bipartite graph. The complexity of the case with k=3 colors is open. Variations and special ...