On the average performance of orthogonal range search in multidimensional data structures
Journal of Algorithms - Analysis of algorithms
On the Average Performance of Orthogonal Range Search in Multidimensional Data Structures
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Expected time analysis for Delaunay point location
Computational Geometry: Theory and Applications
The skip quadtree: a simple dynamic data structure for multidimensional data
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Improving the performance of multidimensional search using fingers
Journal of Experimental Algorithmics (JEA)
ACM Transactions on Algorithms (TALG)
Rank selection in multidimensional data
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Delaunay triangulation of non-uniform point distributions by means of multi-grid insertion
Finite Elements in Analysis and Design
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We modify the k-d tree on [0,1]d by always cutting the longest edge instead of rotating through the coordinates. This modification makes the expected time behavior of lower-dimensional partial match queries behave as perfectly balanced complete k-d trees on n nodes. This is in contrast to a result of Flajolet and Puech [ J. Assoc. Comput. Mach., 33 (1986), pp. 371--407], who proved that for (standard) random k-d trees with cuts that rotate among the coordinate axes, the expected time behavior is much worse than for balanced complete k-d trees. We also provide results for range searching and nearest neighbor search for our trees.