Discrete Optimization

Credits 6 credit points
Instructors Haemers, W. (Universiteit van Tilburg)
E-mail haemers@uvt.nl
Aim To provide an introduction to integer and combinatorial optimization. It treats the basic theory and algorithms.
Description

Integer optimization problems are concerned with the efficient allocation of limited resources to meet desired objectives when the values of the variables are restricted to be integral; in a combinatorial optimization problem the variables have the value 0 or 1.
Integer and combinatorial problems arise in various applications, e.g. airline crew scheduling, manufacturing, communications network design, cellular telephone frequency design and optimization problems on graphs. 

The following subjects are discussed: 

  • Shortest paths and trees. 
  • Bipartite matchings.
  • Assignment problems.
  • Maximal flows and minimal cost flows.
  • Integer linear programming (total unimodularity, cutting planes, branch-and-bound).
  • Introduction to complexity theory (P and NP; polynomial reduction, NP-completeness).
  • Knapsack problems, dynamic programming, traveling salesman problem. 
  • Approximation and heuristics, including performance.
Organization 12 Mondays 10.15 – 12.00 hrs (September 18 – December 4) at Universiteit Utrecht.
Examination To be announced.
Literature
  • Lecture notes: ‘Combinatorial optimization’, Tilburg University.
  • W.J. Cook, W.H. Cunningham, W.R. Pulleyblank and A. Schrijver, ‘Combinatorial Optimization’, Wiley, 1998.
  • C.H. Papadimitriou and K. Steiglitz, ‘Combinatorial Optimization; Algorithms and Complexity’, Prentice-Hall, 1982.
  •  A. Schrijver, 'Combinatorial Optimization - Polyhedra and Efficiency' (Springer-Verlag, Berlin, 2003).
Prerequisites Basic knowledge (bachelor level) of analysis, linear algebra and graph theory.
  Last changed: 18-01-2012 10:21