| Fundamental and applied research in mathematical logic, combinatorics, in particular networks (graphs), optimization, algorithmics, complexity, and transportation. Research topics originate from fields like networks, combinatorial optimization, computational logic and computational complexity, and from practice, in particular: production and transportation planning, routing, scheduling, timetabling, the design of VLSI-circuits, and computational biology. The techniques developed use models and methods from mathematics (mathematical logic, geometry, topology, graph theory), operations research and mathematical optimization (combinatorial, linear, integer, and semidefinite optimization), and computer science (logic and constraint programming and complexity theory). The research within PNA1 is organized through three main subthemes: PNA 1.1 Networks and Optimization (Bert Gerards, Monique Laurent, and Alexander Schrijver): The design, analysis and implementation of optimization and approximation algorithms for combinatorial problems with the help of methods from graph theory, topology, discrete mathematics, geometry, and mathematical optimization. - PNA 1.2 Constraint and Integer Programming (Krzysztof Apt): Foundations and applications of constraint programming. The foundational work concentrates on the design and implementation of an adequate programming environment for constraint programming. The application part concentrates on the use of constraint programming for various optimization problems drawing on integer programming techniques. - PNA1.3 Algorithmic and Combinatorial Methods for Molecular Biology (Leen Stougie): The mathematical analysis of molecular structures in biology and the design, analysis and implementation of algorithms for computational molecular biology. The methods come from combinatorics (graph theory and combinatorial optimization), computer science (constraint programming and computational complexity) and mathematical programming. |
