The team Combinatorics and Algorithms is composed by 4 research groups : Distributed Algorithms, Combinatorics and interactions, Graphs and optimization and Quantum information and computation .
- Distributed algorithmic is the art which aims to organize, make compute, communicate or work together, some computers in a distributed environment, that is in a network with no central authority.
- Combinatorics is the science of discrete structures. In the Enumerative and algebraic combinatorics research group we describe, encode, decompose the basic structures coming from computer science and from other sciences.
- The research group graphs and optimization investigates graphs from a combinatorial perspective, but also design, analyze and optimize graph algorithms.
- The research group Quantum information and computing focus on quantum algorithms, computational speed-up, mathematical optimization, non-commutative algebras, complexity theory, classical simulation of quantum circuits...
Each research group possesses its own seminar, its own activities, but the research teams are so close that the members of the team participate occasionally or permanently to the activities of two or three research groups.
On the research groups web pages, one will find many additional details on the specialties of these groups. Let us add few words on what link them. Distributed algorithmic is deeply related to graph theory since graphs are used to model the communication lines between the processes. Hence, many problems from distributed algorithmic are naturally expressed in terms of graphs, and graph theory tools are determinant to solve them. Conversely, algorithmic problems on large graphs or networks are often solved by distributed algorithmic approach or point of views. Combinatorics help to understand structural and statistical properties of discrete structures. It brings analytical methods which allows one to analyze algorithms, or to understand the right scale of some phenomenons. Finally, one finds in the team many specialties involving members of different research groups : combinatorial optimization, algorithmic geometry, theory of probability, statistical physics, parallel algorithms, combinatorial games, dynamical graphs, dynamical systems, random generation...