McGill University - School of Computer Science

# Algorithms Seminar 2004

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 DATE: Wednesday, March 24th 2004. TIME: 4:30 PM - 5:30 PM PLACE: McConnel 320 TITLE: A quadratic distance bound on sliding between crossing-free spanning trees SPEAKER: Klaus Reinhardt, University of Tuebingen

Let $S$ be a set of $n$ points in the plane in general position and let ${\cal T}_S$ be the set of all crossing-free spanning trees of $S$. We show that it is possible to transform any two trees in ${\cal T}_S$ into each other by $O(n^2)$ local and constant-size edge slide operations. Previously Avis and Fukuda have shown that the corresponding tree graph is connected but no polynomial upper bound for this task was known; in [AichholzerAurenhammerHurtado] a bound of $O(n^2 \log n)$ operations was conjectured. Joint work with Oswin Aichholzer, University of Graz

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