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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.
I, Ivo Vigan, declare that this thesis titled, 'Geometric Separation and Packing Problems' and the work presented in it are my own. I confirm that: This work was done wholly or mainly while in candidature for a research degree at this University. Where any part of this thesis has previously been submitted for a degree or any other qualification at this(More)
We propose to study combinatorial and algorithmic aspects of geometric separation problems in the plane. In such a situation one is given a set of points, line segments or polygons in the plane and a set of separators such as lines, line segments, disks or polygons and the goal is to select a small subset of those separators such that every path between any(More)