


"Mathematical
Challenges in Telecommunication"




Martin
Gr\"otschel


KonradZuseZentrum
f\"ur Informationstechnik


and Technische
Universit\"at Berlin, Germany




Abstract:




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


side.




The presentation
will focus on the problem of


designing
lowcost 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
realworld 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.
