Constructing the Voronoi diagram of a set of line segments in parallel

Algorithmica ◽  
1993 ◽  
Vol 9 (2) ◽  
pp. 128-141 ◽  
Author(s):  
Michael T. Goodrich ◽  
Colm �'D�nlaing ◽  
Chee K. Yap
Keyword(s):  
Voronoi Diagram ◽  
Line Segments

Optimal Parallel Randomized Algorithms for the Voronoi Diagram of Line Segments in the Plane

Algorithmica ◽  
2002 ◽  
Vol 33 (4) ◽  
pp. 436-460 ◽  
Author(s):  
S. Rajasekaran ◽  
S. Ramaswami
Keyword(s):  
Voronoi Diagram ◽  
Randomized Algorithms ◽  
Line Segments

scholarly journals The Higher-Order Voronoi Diagram of Line Segments

Algorithmica ◽  
2014 ◽  
Vol 74 (1) ◽  
pp. 415-439 ◽  
Author(s):  
Evanthia Papadopoulou ◽  
Maksym Zavershynskyi
Keyword(s):  
Voronoi Diagram ◽  
Higher Order ◽  
Line Segments

Dynamic Construction of Voronoi Diagram for a Set of Points and Straight Line Segments

2014 ◽  
Vol 533 ◽  
pp. 264-267
Author(s):  
Xin Liu
Keyword(s):  
Production Process ◽  
Voronoi Diagram ◽  
Voronoi Diagrams ◽  
High Potential ◽  
Line Segments ◽  
Potential Value ◽  
Straight Line ◽  
Traditional Algorithm ◽  
Set Of Points

Voronoi Diagram for a set of points and straight line segments is difficult to construct because general figures have uncertain shapes[. In traditional algorithm, when generator of general figure changes, production process will be extremely complex because of the change of regions neighboring with those generator changed. In this paper, we use dynamicconstruction of Voronoi diagrams. The algorithm can get over all kinds of shortcomings that we have just mentioned. So it is more useful and effective than the traditional algorithm[2]. The results show that the algorithm is both simple and useful, and it is of high potential value in practice.

scholarly journals CONSTRUCTING THE CITY VORONOI DIAGRAM FASTER

2008 ◽  
Vol 18 (04) ◽  
pp. 275-294 ◽  
Author(s):  
ROBERT GÖRKE ◽  
CHAN-SU SHIN ◽  
ALEXANDER WOLFF
Keyword(s):  
Voronoi Diagram ◽  
Transportation Network ◽  
Parallel Line ◽  
Line Segments ◽  
Quickest Path ◽  
Manhattan Metric ◽  
Voronoi Regions ◽  
Axis Parallel ◽  
The City ◽  
And Storage

Given a set P of n point sites in the plane, the city Voronoi diagram subdivides the plane into the Voronoi regions of the sites, with respect to the city metric. This metric is induced by quickest paths according to the Manhattan metric and an accelerating transportation network that consists of c non-intersecting axis-parallel line segments. We describe an algorithm that constructs the city Voronoi diagram (including quickest path information) using O((c+n) polylog (c+n)) time and storage by means of a wavefront expansion. For [Formula: see text] our algorithm is faster than an algorithm by Aichholzer et al., which takes O(n log n + c2 log c) time.

Layout pattern analysis using the Voronoi diagram of line segments

2016 ◽  
Vol 15 (1) ◽  
pp. 013504 ◽  
Author(s):  
Sandeep Kumar Dey ◽  
Panagiotis Cheilaris ◽  
Maria Gabrani ◽  
Evanthia Papadopoulou
Keyword(s):  
Voronoi Diagram ◽  
Pattern Analysis ◽  
Line Segments

scholarly journals THE L∞ VORONOI DIAGRAM OF SEGMENTS AND VLSI APPLICATIONS

2001 ◽  
Vol 11 (05) ◽  
pp. 503-528 ◽  
Author(s):  
EVANTHA PAPADOPOULOU ◽  
D. T. LEE
Keyword(s):  
Voronoi Diagram ◽  
Yield Prediction ◽  
Critical Area ◽  
Vlsi Layout ◽  
Line Segments ◽  
Straight Line ◽  
Computational Bottleneck

In this paper we address the L∞ Voronoi diagram of polygonal objects and present application in VLSI layout and manufacturing. We show that L∞ Voronoi diagram of polygonal objects consists of straight line segments and thus it is much simpler to compute than its Euclidean counterpart; the degree of the computation is significantly lower. Moreover, it has a natural interpretation. In applications where Euclidean precision is not essential the L∞ Voronoi diagram can provide a better alternative. Using the L∞ Voronoi diagram of polygons we address the problem of calculating the critical area for shorts in a VLSI layout. The critical area computation is the main computational bottleneck in VLSI yield prediction.

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