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Binary Search Trees of Almost Optimal Height
 ACTA INFORMATICA
, 1990
"... First we present a generalization of symmetric binary Btrees, SBB(k) trees. The obtained structure has a height of only \Sigma (1 + 1k) log(n + 1)\Upsilon, where k may be chosen to be any positive integer. The maintenance algorithms require only a constant number of rotations per updating operati ..."
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First we present a generalization of symmetric binary Btrees, SBB(k) trees. The obtained structure has a height of only \Sigma (1 + 1k) log(n + 1)\Upsilon, where k may be chosen to be any positive integer. The maintenance algorithms require only a constant number of rotations per updating operation in the worst case. These properties together with the fact that the structure is relatively simple to implement makes it a useful alternative to other search trees in practical applications. Then, by using an SBB(k)tree with a varying k we achieve a structure with a logarithmic amortized cost per update and a height of log n + o(log n). This result is an improvement of the upper bound on the height of a dynamic binary search tree. By maintaining two trees simultaneously the amortized cost is transformed into a worstcase cost. Thus, we have improved the worstcase complexity of the dictionary problem.
Comparisonefficient and writeoptimal searching and sorting
 In ISA'91, volume 557 of LNCS
, 1991
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Optimal bounds on the dictionary problem
 In Proc. Symp. on Optimal Algorithms, Varna, volume 401 of LNCS
, 1989
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1 A Tutorial on Spatial Data Handling
"... Spatial data is data related to space. In various application fields like GIS, multimedia information systems, etc., there is a need to store and manage these data. Some datastructures used for the spatial access methods are R tree and its extensions where objects could be approximated by their mini ..."
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Spatial data is data related to space. In various application fields like GIS, multimedia information systems, etc., there is a need to store and manage these data. Some datastructures used for the spatial access methods are R tree and its extensions where objects could be approximated by their minimum bounding rectangles and Quad tree based structures where space is subdivided according to certain rules. Also another structure KD Tree is used for organizing points in a k dimensional space. This paper makes review on some of these Hiearchical datastructures used for handling point data. It focuses on PR Quad Tree and KD Tree.The insertion procedure of these structures is reviewed and analyzed and also a comparison between them is drawn..