Range-aggregate queries for geometric extent problems

Authors:
Peter Brass;Christian Knauer;Chan-Su Shin;Michiel Smid;Ivo Vigan
Affiliations:
The City College of New York, New York, NY;Universität Bayreuth, Bayreuth, Germany;Hankuk University of Foreign Studies, Yongin, Korea;Carleton University, Ottawa, Ontario, Canada;City University of New York, The Graduate Center, New York, NY
Venue:
CATS '13 Proceedings of the Nineteenth Computing: The Australasian Theory Symposium - Volume 141
Year:
2013

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Abstract

Let S be a set of n points in the plane. We present data structures that solve range-aggregate query problems on three geometric extent measure problems. Using these data structures, we can report, for any axis-parallel query rectangle Q, the area/perimeter of the convex hull, the width, and the radius of the smallest enclosing disk of the points in S ∩ Q.