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 -