# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, September 25, 2007, 12:15 pm

**Duration**: This information is not available in the database

**Location**: CAB G51

**Speaker**: Rico Zenklusen

## High-Confidence Estimation of Small s-t Reliabilities in Acyclic Networks

In the classical s-t network reliability problem a fixed network G is
given including two designated vertices s and t (called terminals). The
edges are subject to independent random failure, and the task is to
compute the probability that s and t a re connected in the resulting
network, which is known to be #P-complete. In this talk, I will discuss
the issue of approximating the s-t reliability in case of a directed
acyclic original network G. A specialized version of a Monte-Carlo
algorithm given by Karp and Luby will be introduced and analyzed. For
the case of uniform edge failure probabilities, I will present a
worst-case bound on the number of samples that have to be drawn to
obtain an epsilon-delta approximation, being sharper than the original
upper bound. Computational results on two types of random networks
(directed acyclic Delaunay graphs and a slightly modified version of a
classical random graph) with up to one million vertices are presented.
These results show the advantage of the introduced Monte-Carlo approach
compared to direct simulation when small reliabilities have to be
estimated and demonstrate its applicability on large-scale instances.
Furthermore, applications to spreading processes on networks will be
highlighted.

Joint work with Marco Laumanns.

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