Ph.D
Group : Graphs, ALgorithms and Combinatorics

A few algorithmic and complexity problems in graph theory

Starts on 01/10/2013
Advisor : MANOUSSAKIS, Yannis

Funding : Aucun financement
Affiliation : Université Paris-Saclay
Laboratory : LRI - GALaC

Defended on 01/03/2017, committee :

Research activities :

Abstract :
This thesis is about graph theory. Formally, a graph is a set of vertices and a set of edges, which are pair of vertices, linking vertices. This thesis deals with various decision problem linked to the notion of graph, and, for each of these problem, try to find its complexity class, or to give an algorithm.

The first chapter is about the problem of finding the smallest connected tropical subgraph of a vertex-colored graph, which is the smallest connecter subgraph containing every colors.

The second chapter is about problems of tropical homomorphism, a generalisation of coloring problem. A link between these problems and several other class of homomorphism problems can be found in this chapter, especially with the class of Constraint Satisfaction Problem.

The third chapter is about two variant of the domination problem, namely the global alliance problems in a weighted graph and the safe set problem.

The fourth chapter is about the problem of finding a star tree-decomposition, which is a tree-decomposition where the radius of bags is 1.

Finally, the fifth chapter is about a variant of the problem of deciding the asymptotic behavior of the iterated biclique graph.

CAUSAL LEARNING FOR DIAGNOSTIC SUPPORT


CAUSAL UNCERTAINTY QUANTIFICATION UNDER PARTIAL KNOWLEDGE AND LOW DATA REGIMES


MICRO VISUALIZATIONS: DESIGN AND ANALYSIS OF VISUALIZATIONS FOR SMALL DISPLAY SPACES
The topic of this habilitation is the study of very small data visualizations, micro visualizations, in display contexts that can only dedicate minimal rendering space for data representations. For several years, together with my collaborators, I have been studying human perception, interaction, and analysis with micro visualizations in multiple contexts. In this document I bring together three of my research streams related to micro visualizations: data glyphs, where my joint research focused on studying the perception of small-multiple micro visualizations, word-scale visualizations, where my joint research focused on small visualizations embedded in text-documents, and small mobile data visualizations for smartwatches or fitness trackers. I consider these types of small visualizations together under the umbrella term ``micro visualizations.'' Micro visualizations are useful in multiple visualization contexts and I have been working towards a better understanding of the complexities involved in designing and using micro visualizations. Here, I define the term micro visualization, summarize my own and other past research and design guidelines and outline several design spaces for different types of micro visualizations based on some of the work I was involved in since my PhD.