By Topic

On 2-Site Voronoi Diagrams under Arithmetic Combinations of Point-to-Point Distances

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Vyatkina, K. ; Dept. of Math. & Mech., St. Petersburg State Univ., St. Petersburg, Russia ; Barequet, G.

We consider a generalization of Voronoi diagrams, recently introduced by Barequet et al., in which the distance is measured from a pair of sites to a point. An easy way to define such distance was proposed together with the concept: it can be the sum-of, the product-of, or (the absolute value of) the difference-between Euclidean distances from either site to the respective point. We explore further the last definition, and analyze the complexity of the nearest- and the furthest-neighbor 2-site Voronoi diagrams for points in the plane with Manhattan or Chebyshev underlying metrics, providing extensions to general Minkowsky metrics and, for the nearest-neighbor case, to higher dimensions. In addition, we point out that the observation made earlier in the literature that 2-point site Voronoi diagrams under the sum-of and the product-of Euclidean distances are identical and almost identical to the second order Voronoi diagrams, respectively, holds in a much more general statement.

Published in:

Voronoi Diagrams in Science and Engineering (ISVD), 2010 International Symposium on

Date of Conference:

28-30 June 2010