Section: Research Program
Members of Coati have a strong expertise in the design and management of wired and wireless backbone, backhaul, broadband, software defined and complex networks. On the one hand, we cope with specific problems such as energy efficiency in backhaul and backbone networks, routing reconfiguration in connection oriented networks (mpls , wdm ), traffic aggregation in sonet networks, compact routing in large-scale networks, survivability to single and multiple failures, etc. These specific problems often come from questions of our industrial partners. On the other hand, we study fundamental problems mainly related to routing and reliability that appear in many networks (not restricted to our main fields of applications) and that have been widely studied in the past. However, previous solutions do not take into account the constraints of current networks/traffic such as their huge size and their dynamics. Coati thus puts a significant research effort in the following directions:
Service Function Chains (SFC): we study the placement of Service Function Chains within the network considering the ordering constraints. Then, we focus firstly on energy efficiency and secondly on reliability and protection mechanisms. In a last step, we study reconfiguration of the SFCs in case of dynamic traffic with a make-before-break approach.
Larger networks: Another challenge one has to face is the increase in size of practical instances. It is already difficult, if not impossible, to solve practical instances optimally using existing tools. Therefore, we have to find new ways to solve problems using reduction and decomposition methods, characterization of polynomial instances (which are surprisingly often the practical ones), or algorithms with acceptable practical performances.
Stochastic behaviors: Larger topologies mean frequent changes due to traffic and radio fluctuations, failures, maintenance operations, growth, routing policy changes, etc. We aim at including these stochastic behaviors in our combinatorial optimization process to handle the dynamics of the system and to obtain robust designs of networks.
The methods and tools used in our studies come from discrete mathematics and combinatorial optimization, and Coati contributes to their improvements. Also, Coati works on graph-decomposition methods and various games on graphs which are essential for a better understanding of the structural and combinatorial properties of the problems, but also for the design of efficient exact or approximate algorithms. We contribute to the modelling of optimization problems in terms of graphs, study the complexity of the problems, and then we investigate the structural or metric properties of graphs that make these problems hard or easy. We exploit these properties in the design of algorithms in order to find the most efficient ways for solving the problems.
Coati also focuses on the theory of directed graphs. Indeed, graph theory can be roughly partitioned into two branches: the areas of undirected graphs and directed graphs. Even though both areas have numerous important applications, for various reasons, undirected graphs have been studied much more extensively than directed graphs. It is worth noticing that many telecommunication problems are modelled with directed graphs. Therefore, a deeper understanding of the theory of directed graphs will benefit to the resolution of telecommunication networks problems. For instance, the problem of finding disjoint paths becomes much more difficult in directed graphs and understanding the underlying structures of actual directed networks would help us to propose solutions.
Last, we have recently started investigating how tools from multi-agents based systems and machine learning theory could help solving some optimization problems in networks. The arrival of Emanuele Natale as a Junior Researcher (CNRS) in the team and of two new PhD students (Franceso D'Amore and Hicham Lesfari) will foster these investigations.