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

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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

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)

Linear time algorithms for geodesic problems on simple polygons

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