Theme Algorithmics, Graphs, Complexity

Presentation

The main research areas of the team can be classified into two parts : (1) structural graph/lattice theory and the consequences in algorithmics, and (2) algorithmic geometry with a main focus on discrete convexity.

It is usual when studying discrete objects to follow the advice of Descartes, namely divide and conquer, i.e., define operators on discrete objects and decompose with respect to these operators in order to explain their inherent complexity. The team has a strong expertise in studying structural graph/lattice theory through the lens of graph/lattice decompositions and their applications in several algorithmic questions and in combinatorics. Some examples of graph decompositions studied in this group are tree-decomposition, rank-decomposition and understanding when the associated width measures are bounded in some graph classes, and also decompositions based on cut set such as clique and stable-cut set and skew partitions with applications in colouring graphs. Some examples of decompositions in lattices are recursive constructions based on copying convex sets or based on colored posets. Some other applications of the studied decompositions can be:

  • Listing problems in (hyper)graphs and lattices. We have a strong expertise in the listing of vertex subsets of a hypergraph satisfying a property. We have, for instance, and proved that the listing of minimal dominating sets is equivalent to the well-known Hypergraph Dualisation problem. 
  • Representation of lattices and efficient algorithms on lattices. This question is mainly studied with respect to the Lattice Dualisation problem, a particular case of which is the Hypergraph Dualisation Problem. 
  • Optimisation problems in (hyper)graphs. Studied problems include, but are not limited to, colouring problems, graph identification problems, homomorphism questions, etc. We are mostly interested in obtaining either tight bounds on some parameters such as chromatic number or identifying codes, or tight time complexities parametrised by complexity measures. 
  • Packing and covering problems such as Erdös-Posa functions. 

The main interests in algorithmic geometry deal with computational aspects in digital/discrete geometry such as the computation of convex hulls in digitall euclidean spaces. The members are experts in designing heuristics for obtaining competetive algorithms for computing (approximate) convex hulls for various configurations of points in the 2D euclidean space (many of such problems are NP-hard ones). Members often participate to the CG:SHOP challenge, organised during SoCG conference, and win the 2021 edition which were about the coordinated robot motion planning.

Keywords: graph theory; graph complexity parameters; graph decompositions; algorithmic lattice theory; algorithmic geometry; discrete convexity; listing/enumerating algorithms;

Last publications

Arun Kumar Das, Sandip Das, Guilherme D. da Fonseca, yan Gerard, Bastien Rivier - Feb. 25, 2022
Complexity Results on Untangling Planar Rectilinear Red-Blue Matchings


Lhouari Nourine, Simon Vilmin - Feb. 11, 2022
The enumeration of meet-irreducible elements based on hierarchical decompositions of implicational bases


Mohammed Elaroussi, Lhouari Nourine, Mohammed Said Radjef, Simon Vilmin - Feb. 11, 2022
On the preferred extensions of argumentation frameworks: bijections with naive extensions


Florent Foucaud, Hervé Hocquard, Dimitri Lajou, Valia Mitsou, Théo Pierron - Jan. 4, 2022
Graph Modification for Edge-Coloured and Signed Graph Homomorphism Problems: Parameterized and Classical Complexity
Algorithmica

Fabien Feschet, Antoine Vacavant, Bertrand Kerautret - Nov. 25, 2021
Robust reconstructions by multi-scale/irregular tangential covering


Laurent Beaudou, Caroline Brosse, Oscar Defrain, Florent Foucaud, Aurélie Lagoutte, Vincent Limouzy, Lucas Pastor - Oct. 28, 2021
Connected greedy colourings of perfect graphs and other classes: the good, the bad and the ugly


Florent Foucaud, Benjamin Gras, Anthony Perez, Florian Sikora - Sept. 1, 2021
On the Complexity of Broadcast Domination and Multipacking in Digraphs
Algorithmica

Florent Foucaud, Hervé Hocquard, Dimitri Lajou - Sept. 1, 2021
Complexity and algorithms for injective edge-coloring in graphs
Information Processing Letters

Thomas Bellitto, Caroline Brosse, Benjamin Lévêque, Aline Parreau - Aug. 31, 2021
Locating Dominating Sets in local tournaments


Simon Coumes, Tassadit Bouadi, Lhouari Nourine, Alexandre Termier - July 5, 2021
Skyline Groups Are Ideals. An Efficient Algorithm for Enumerating Skyline Groups
IWOCA 2021 - 32nd International Workshop on Combinatorial Algorithms

All publications are here