This involves fundamental research to address complex graph problems in network science. We tackle challenges related to graph modeling, routing, and network optimization amongst others. In this space, we explore combinatorial and geometric problems such as network planning and scheduling. Our expertise extends to both discrete and continuous optimization and simulation, encompassing online and offline settings. Additionally, we delve into the design and analysis of related data structures. By combining insights from mathematics and computer science (graph theory, linear programming, AI e.g. meta-heuristics), we strive to create next-generation algorithms that find optimal solutions amidst vast possibilities, analyze their performance and prove their correctness. In our pursuit of efficient solutions for complex network challenges, we harness the power of graph theory as a framework for modeling and optimizing various network scenarios. For instance, in network flow problems, specifically tailored graph algorithms allow us to optimize routing and to allocate resources while respecting capacity and delay constraints.
