Monday, December 12, 2011
Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136, 10623 Berlin
room MA 041
Lecture - 14:15
Given a network with a single source and several sinks with associated demands, we study flow problems with restrictions on the flow-carrying paths. In the unsplittable flow problem, the demand of each sink has to be satisfied along a single source-sink path. The k-splittable flow problem allows to split each demand into at most k packets such that each packet is sent along a single source-sink path. We discuss recent results and algorithms for turning an arbitrary flow into an unsplittable or k-splittable flow with bounded increase of flow values along arcs.
Colloquium - 16:00
It is a simple fact that each lattice possesses a fundamental cell (wrt to translations) whose symmetry group is the point group of the lattice: just take the Voronoi cell of some lattice point. It is kind of surprising that there are fundamental domains for certain lattices which possess more symmetry than the point group of the corresponding lattice. In this talk it is shown that "almost all" lattices in dimension 2 and 3 have fundamental cells of higher symmetry than their point group (and it is explained what "almost all" means in this case). The talk is accompanied by several nice pictures.