"Mathematical Challenges in Telecommunication"

Martin Gr\"otschel
Konrad-Zuse-Zentrum f\"ur Informationstechnik
and Technische Universit\"at Berlin, Germany


This talk will begin with a survey of mathematical
challenges that arise in telecommunication. Mathematics
is involved, e. g., in the design and manufacturing of
chips, devices and network components, the choice
of locations, the planning of the network topology,
and the dimensioning of the equipment involved.
Adequate cryptography, the need of fast data processing,
demand routing and failure handling require efficient
and reliable mathematical algorithms on the operational

The presentation will focus on the problem of
designing low-cost telecommunication networks that
provide sufficient capacity to serve a given demand,
are based on a chosen technology mix, satisfy various
technical side constraints, and survive certain
failure situations. This problem is difficult
in theory and practice. It will be indicated how
algorithms integrating polyhedral combinatorics, linear
and integer programming, and various heuristic ideas can
help solve real-world instances within reasonable quality
guarantees in acceptable running times.

The lecture will also address issues such as: balancing
the load of signaling transfer points, issues arising
in packet switching, modeling optical switches and
all optical networks.networks

This talk is based on work of the telecommunications
research group at ZIB, the examples discussed and
the computational results reported are from joint
projects with several telecommunication companies.