Box-trees and R-trees with near-optimal query time

P.K. Agarwal, M. Berg, de, J. Gudmundsson, M. Hammar, H.J. Haverkort

    Research output: Contribution to journalArticleAcademicpeer-review

    41 Citations (Scopus)


    A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. The query complexity of a box-tree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing box-trees with small worst-case query complexity with respect to queries with axis-parallel boxes and with points. We also prove lower bounds on the worst-case query complexity for box-trees, which show that our results are optimal or close to optimal. Finally, we present algorithms to convert box-trees to R-trees, resulting in R-trees with (almost) optimal query complexity.
    Original languageEnglish
    Pages (from-to)291-312
    JournalDiscrete and Computational Geometry
    Issue number3
    Publication statusPublished - 2002


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