Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, November 08, 2016, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Daniel Graf

In the 2-reachability problem we are given a directed graph G and we wish to determine if there are two (edge or vertex) disjoint paths from u to v, for every pair of vertices u and v. In this talk, we present an algorithm that computes 2-reachability information for all pairs of vertices in $O(n^{\omega}\log n)$ time, where n is the number of vertices and $\omega$ the matrix multiplication exponent. Hence, rather surprisingly, we show that the running time of 2-reachability is within a log-factor of transitive closure.

Moreover, our algorithm produces a witness (separating edge or separating vertex) whenever 2-reachability does not hold. By processing these witnesses, we can compute all the edge- and vertex-dominator trees of G in $O(n^2)$ additional time, which in turn enables us to answer various connectivity queries in O(1) time. For instance, we can test in constant time if there is a path from u to v avoiding an edge e, for any pair of query vertices u and v, and any query edge e, or if there is a path from u to v avoiding a vertex w, for any query vertices u, v and w.

This is joint work with Loukas Georgiadis, Giuseppe F. Italiano, Nikos Parotsidis and Przemysław Uznański.

Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)

Previous talks by year: 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M | admin login