Optimal Distributed Algorithms in Unlabelled Tori and Chordal Rings

We study the message complexity of distributed algorithms in Tori and Chordal Rings when the communication links are unlabelled, which implies that the processors do not have a globally consistent labelling of the communication links. They have no "Sense of Direction" but have only a topological awareness. We use a preprocessing algorithm to introduce the notion of handrail, a partial structural information, which allows messages to travel with a "globally consistent direction". Hence, we give a distributed algorithm which confirms the conjecture suggested in [12] that the Leader Election problem for unlabelled Tori of N processors can be solved using \Theta(N ) messages instead of O(N log N ). Using the same handrail paradigm, we solve the Election problem using \Theta(N ) messages in unlabelled chordal rings with one chord (of length approximately p N ). This solves a longstanding open problem [2] of the minimal number of chords and minimal Sense of Direction required to decrease t..

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes