Computing rectangle enclosures

Abstract

The rectangle enclosure problem is the problem of determining the subset of n iso-oriented planar rectangles that enclose a query rectangle Q. In this paper, we use a three layered data structure which is a combination of Range and Priority search trees and answers both the static and dynamic cases of the problem. Both the cases use O( n> log 2 n) space. For the static case, the query time is O( log 2 n log log n + K). The dynamic case is supported in O( log 3 n + K) query time using O( log 3 n) amortized time per update. K denotes the size of the answer. For the d-dimensional space the results are analogous. The query time is O( log 2 d-2 n log log n + K) for the static case and O( log 2 d-1 n + K) for the dynamic case. The space used is O( n> log 2 d-2 n) and the amortized time for an update is O( log 2 d-1 n). The existing bounds given for a class of problems which includes the present one, are O( log 2 d n + K) query time, O( log 2 d n) time for an insertion and O( log 2 d-1 n) time for a deletion.