TY - GEN

T1 - On dynamic voronoi diagrams and the minimum hausdorff distance for points sets under Euclidean motion in the plane

AU - Huttenlocher, Daniel P.

AU - Kedem, Klara

AU - Kleinberg, Jon M.

PY - 1992/12/1

Y1 - 1992/12/1

N2 - We show that the dynamic Voronoi diagram of K sets of points in the plane, where each set consists of n points moving rigidly, has complexity O(n2κ2λs(κ)) for some fixed s, where λs(n) is the maximum length of a (n,s) Davenport-Schinzel sequence. This improves the result of Aonuma et. al., who show an upper bound of O(n3κ4log k) for the complexity of such Voronoi diagrams. We then apply this result to the problem of finding the minimum Hausdorff distance between two points sets in the plane under Euclidean motion. We show that this distance can be computed in time O((m + n)6 log(mn)), where the two sets contain m and n points respectively.

AB - We show that the dynamic Voronoi diagram of K sets of points in the plane, where each set consists of n points moving rigidly, has complexity O(n2κ2λs(κ)) for some fixed s, where λs(n) is the maximum length of a (n,s) Davenport-Schinzel sequence. This improves the result of Aonuma et. al., who show an upper bound of O(n3κ4log k) for the complexity of such Voronoi diagrams. We then apply this result to the problem of finding the minimum Hausdorff distance between two points sets in the plane under Euclidean motion. We show that this distance can be computed in time O((m + n)6 log(mn)), where the two sets contain m and n points respectively.

UR - http://www.scopus.com/inward/record.url?scp=0026976786&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0026976786

SN - 0897915178

T3 - Eighth Annual Symposium On Computational Geometry

SP - 110

EP - 119

BT - Eighth Annual Symposium On Computational Geometry

PB - Publ by ACM

T2 - Eighth Annual Symposium On Computational Geometry

Y2 - 10 June 1992 through 12 June 1992

ER -