TY - GEN
T1 - A randomized incremental approach for the hausdorff voronoi diagram of non-crossing clusters
AU - Cheilaris, Panagiotis
AU - Khramtcova, Elena
AU - Langerman, Stefan
AU - Papadopoulou, Evanthia
PY - 2014/1/1
Y1 - 2014/1/1
N2 - In the Hausdorff Voronoi diagram of a set of point-clusters in the plane, the distance between a point t and a cluster P is measured as the maximum distance between t and any point in P, and the diagram reveals the nearest cluster to t. This diagram finds direct applications in VLSI computer-aided design. In this paper, we consider "non-crossing" clusters, for which the combinatorial complexity of the diagram is linear in the total number n of points on the convex hulls of all clusters. We present a randomized incremental construction, based on point-location, to compute the diagram in expected O(n log2 n) time and expected O(n) space, which considerably improves previous results. Our technique efficiently handles non-standard characteristics of generalized Voronoi diagrams, such as sites of non-constant complexity, sites that are not enclosed in their Voronoi regions, and empty Voronoi regions.
AB - In the Hausdorff Voronoi diagram of a set of point-clusters in the plane, the distance between a point t and a cluster P is measured as the maximum distance between t and any point in P, and the diagram reveals the nearest cluster to t. This diagram finds direct applications in VLSI computer-aided design. In this paper, we consider "non-crossing" clusters, for which the combinatorial complexity of the diagram is linear in the total number n of points on the convex hulls of all clusters. We present a randomized incremental construction, based on point-location, to compute the diagram in expected O(n log2 n) time and expected O(n) space, which considerably improves previous results. Our technique efficiently handles non-standard characteristics of generalized Voronoi diagrams, such as sites of non-constant complexity, sites that are not enclosed in their Voronoi regions, and empty Voronoi regions.
UR - https://www.scopus.com/pages/publications/84899926718
U2 - 10.1007/978-3-642-54423-1_9
DO - 10.1007/978-3-642-54423-1_9
M3 - Conference contribution
AN - SCOPUS:84899926718
SN - 9783642544224
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 96
EP - 107
BT - LATIN 2014
PB - Springer Verlag
T2 - 11th Latin American Theoretical Informatics Symposium, LATIN 2014
Y2 - 31 March 2014 through 4 April 2014
ER -