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: Thursday, October 06, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Matias Korman (Tohoku University)

Time-Space Trade-offs for Computing (High Order) Voronoi Diagrams

Let P be a planar n-point set in general position. For any k (up to n-1), the Voronoi diagram of order k is obtained by subdividing the plane into regions such that points in the same cell have the same set of nearest k neighbors in P. The nearest point Voronoi diagram (NVD) and farthest point Voronoi diagram (FVD) are the particular cases of k=1 and k=n-1. It is known that the Voronoi diagram of orders 1 to k for P can be computed in total time O(nk^2+ n log n) using O(n) space (or O(n log n) time for FVD).

For s up to n, an s-workspace algorithm has random access to a read-only array with the sites of P in arbitrary order. Additionally, the algorithm may use O(s) words of Theta(log n) bits each for reading and writing intermediate data. The output can be written only once and cannot be accessed afterwards.

We describe a deterministic s-workspace algorithm for computing an NVD and also an FVD for P that runs in O((n^2/s) log s) time. Moreover, we generalize our algorithm for computing the family of all higher-order Voronoi diagrams of P up to order K=O(sqrt(s)) in total time O(n^2 K^6 polylog(K,s)).

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