Ph.D
Group : Graphs, ALgorithms and Combinatorics

A guide book for the traveller on graphs full of blockages

Starts on
Advisor : TOMASIK, Joanna

Funding :
Affiliation : Université Paris-Saclay
Laboratory : l'amphi IV du bâtiment Eiffel de CentraleSupélec

Defended on 03/12/2019, committee :

Research activities :

Abstract :
We study NP-hard problems dealing with graphs containing blockages.

We analyze cut problems via the parameterized complexity framework. The size p of the cut is the parameter. Given a set of sources {s_1,...,s_k} and a target t, we propose an algorithm deciding whether a cut of size at most p separates at least r sources from t. This problem is called Partial One-Target Cut. Our algorithm is FPT. We also prove that the vertex version of the problem, where the cut contains vertices instead of edges, is W[1]-hard. Our second contribution is an algorithm counting minimum (S,T)-cuts in time 2^{O(p log p)}n^{O(1)}.

Then, we present numerous results on the competitive ratio of deterministic and randomized strategies for the Canadian Traveller Problem. We show that randomized strategies which do not use memory cannot improve the ratio 2k+1. We also provide theorems on the competitive ratio of randomized strategies in general. We study the distance competitive ratio of a group of travellers with and without communication. Eventually, we treat the competitiveness of deterministic strategies dedicated to certain families of graphs. Two strategies with a ratio below 2k+1 are proposed: one for equal-weight chordal graphs and another one for graphs such that the largest minimal (s,t)-cut is at most k.

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.