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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, May 12, 2015, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Luis Barba (Carleton University / Université Libre de Bruxelles)

Let $P$ be a closed simple polygon with $n$ vertices. For any two points in $P$, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in $P$.

The geodesic center of $P$ is the unique point in $P$ that minimizes the largest geodesic distance to all other points of $P$. In 1989, Pollack, Sharir and Rote [Disc. & Comput. Geom. 89] showed an $O(n\log n)$-time algorithm that computes the geodesic center of $P$. Since then, a longstanding question has been whether this running time can be improved (explicitly posed by Mitchell [Handbook of Computational Geometry, 2000]). In this talk, we affirmatively answer this question and present a linear time algorithm to solve this problem.

Extending the techniques used by this algorithm, we study the following problem: Given a set $S\subset \partial P$ of $m$ sites sorted in clockwise order along $\partial P$, compute the geodesic farthest-point Voronoi diagram of $S$. Aronov et al. [Disc. & Comput. Geom. 93] showed how to compute this diagram in $O((n+m) \log (n+m))$ time. In this talk, we improve this result and show how to obtain this diagram in $O(n + m)$ time.

This is joint work with Hee-Kap Ahn, Prosenjit Bose, Jean-Lou De Carufel, Matias Korman and Eunjin Oh.

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

Previous talks by year: 2024 2023 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