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The L_infinity (L_1) Farthest Line-Segment Voronoi Diagram

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2 Author(s)
Dey, S.K. ; Fac. of Inf., Univ. della Svizzera Italiana, Lugano, Switzerland ; Papadopoulou, E.

We present structural properties of the farthest line-segment Voronoi diagram in the piecewise linear L and L1 metrics, which are computationally simpler than the standard Euclidean distance and very well suited for VLSI applications. We introduce the farthest line-segment hull, a closed polygonal curve that characterizes the regions of the farthest line-segment Voronoi diagram, and is related to it similarly to the way an ordinary convex hull relates to the farthest-point Voronoi diagram. In L (resp. L1) the farthest line-segment hull, and thus the farthest line-segment Voronoi diagram, has size O(h), where h ranges from O(1) e.g., axis parallel line-segments, to O(n), and it can be constructed in time O(n log h). Once the L (resp. L1) farthest line-segment hull is available, the corresponding Voronoi diagram can be constructed in additional O(h) time.

Published in:

Voronoi Diagrams in Science and Engineering (ISVD), 2012 Ninth International Symposium on

Date of Conference:

27-29 June 2012