| [home] - [up] |
Abstract: A knot is a simple closed curve embedded in 3-space. The fundamental algorithmic problem in knot theory is to decide whether two given knots are equivalent. It contains as a special case the unknotting problem. A result of Reidemeister from 1932 implies that these problems, which are problems in computational topology, can be formulated as purely combinatorial problems. In this talk we will survey known results on the computational complexity of these two problems. We also give a brief introduction to knot polynomials which are a powerful tool to distinguish knots. Finally we discuss the problem of enumerating all knots up to a given crossing number.
Colloquium - 16:00
Abstract: Third generation telecommunication networks based on UMTS technology are currently rolled-out across Europe. Radio network planning is an important task in this context. The WCDMA technology employed for UMTS radio access differs significantly from traditional GSM networks, experiences from 2G planning are therefore only useful to a limited extent.
The task in radio network design is to find a combination of antenna configurations that produce a "good" radio network for a given stochastic load distribution. An important aspect is the control of interference. In this talk, we introduce network design problems and related mathematical models. Based on these models, we treat analytical and practical solution approaches and results.