Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

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

Duration: This information is not available in the database

Location: OAT S15/S16/S17

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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