TY - GEN
T1 - Voronoi diagram for convex polygonal sites with convex polygon-offset distance function
AU - Barequet, Gill
AU - De, Minati
N1 - Publisher Copyright: © Springer International Publishing AG 2017.
PY - 2017
Y1 - 2017
N2 - The concept of convex polygon-offset distance function was introduced in 2001 by Barequet, Dickerson, and Goodrich. Using this notion of point-to-point distance, they showed how to compute the corresponding nearest- and farthest-site Voronoi diagram for a set of points. In this paper we generalize the polygon-offset distance function to be from a point to any convex object with respect to an m-sided convex polygon, and study the nearest- and farthest-site Voronoi diagrams for sets of line segments and convex polygons. We show that the combinatorial complexity of the nearest-site Voronoi diagram of n disjoint line segments is O(nm), which is asymptotically equal to that of the Voronoi diagram of n point sites with respect to the same distance function. In addition, we generalize this result to the Voronoi diagram of disjoint convex polygonal sites. We show that the combinatorial complexity of the nearest-site Voronoi diagram of n convex polygonal sites, each having at most k sides, is O(n(m + k)). Finally, we show that the corresponding farthest-site Voronoi diagram is a tree-like structure with the same combinatorial complexity.
AB - The concept of convex polygon-offset distance function was introduced in 2001 by Barequet, Dickerson, and Goodrich. Using this notion of point-to-point distance, they showed how to compute the corresponding nearest- and farthest-site Voronoi diagram for a set of points. In this paper we generalize the polygon-offset distance function to be from a point to any convex object with respect to an m-sided convex polygon, and study the nearest- and farthest-site Voronoi diagrams for sets of line segments and convex polygons. We show that the combinatorial complexity of the nearest-site Voronoi diagram of n disjoint line segments is O(nm), which is asymptotically equal to that of the Voronoi diagram of n point sites with respect to the same distance function. In addition, we generalize this result to the Voronoi diagram of disjoint convex polygonal sites. We show that the combinatorial complexity of the nearest-site Voronoi diagram of n convex polygonal sites, each having at most k sides, is O(n(m + k)). Finally, we show that the corresponding farthest-site Voronoi diagram is a tree-like structure with the same combinatorial complexity.
KW - Convex polygonal sites
KW - Farthest-site voroni diagram
KW - Line segments
KW - Nearest-site voroni diagram
KW - Polygon-offset distance function
UR - http://www.scopus.com/inward/record.url?scp=85012248831&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-53007-9_3
DO - 10.1007/978-3-319-53007-9_3
M3 - منشور من مؤتمر
SN - 9783319530062
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 24
EP - 36
BT - Algorithms and Discrete Applied Mathematics - 3rd International Conference, CALDAM 2017, Proceedings
A2 - Narayanaswamy, N.S.
A2 - Gaur, Daya
T2 - 3rd International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2017
Y2 - 16 February 2017 through 18 February 2017
ER -