#
Monday Lecture and Colloquium

**Monday, May 9, 2011**

Humboldt-Universität zu Berlin

Institut für Informatik

Rudower Chaussee 25

12489 Berlin

room 3.113
(1. Etage, Haus 3)

** Lecture - 14:15**

### Rob van Stee - Max Planck Institut für Informatik, Saarbrücken

### Truthful approximations for maximizing the minimum load

*Abstract:*

Designing truthful mechanisms for scheduling on related
machines is a very important problem in single-parameter mechanism
design. We consider the covering objective, that is we are
interested in maximizing the minimum completion time of a
machine. This problem falls into the class of problems where the
optimal allocation can be truthfully implemented. A major open issue for
this class is whether truthfulness affects the polynomial-time
implementation.

We provide the first constant factor approximation for deterministic
truthful mechanisms.

In particular we come up with a approximation guarantee of 2+epsilon
for any epsilon>0, significantly improving on the previous upper bound
of min(m,(2+epsilon)s_m/s_1). Here m is the number of machines and s_i
is the speed of machine i for i=1,...,m.

**Colloquium - 16:00**

###
Piotr Sankowski - University of Warsaw

###
Min st-cut oracle for planar graphs with near-linear preprocessing time

*Abstract:*

For an undirected n-vertex planar graph G with non-negative
edge-weights, we consider the following type of query: given two
vertices s and t in G, what is the weight of a min st-cut in G? We
show how to answer such queries in constant time with O(n log^5 n)
preprocessing time and O(n log n) space. We use a Gomory-Hu tree to
represent all the pairwise min st-cuts implicitly. Previously, no
subquadratic time algorithm was known for this problem. Our oracle can
be extended to report the min st-cuts in time proportional to their
size. Since all-pairs min st-cut and the minimum cycle basis are dual
problems in planar graphs, we also obtain an implicit representation
of a minimum cycle basis in O(n log^5 n) time and O(n log n) space and
an explicit representation with additional O(C) time and space where C
is the size of the basis. To obtain our results, we require that
shortest paths be unique; this assumption can be removed
deterministically with an additional O(log^2 n) running-time factor.

Joint work with Glencora Borradaile and Christian Wulff-Nilsen.

Letzte Aktualisierung:
05.05.2011