Abstract
Our main result is that space O[N(log N / log log N)k−1] suffices for either doing dynamic k-dimensional aggregate orthogonal range queries in time O(logkN) on a set of N records, or for arbitrary ∈>0 to do static aggregate queries in time O(logk−1+εN). This result improves upon the memory space used by slightly more than one dozen previous authors by a factor O[(log log N)k−1], and it has applications to rectangle intersection problems, VLSI-design, relational data bases, and queries about the past.
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Dan Willard, E. (1984). Reduced memory space for multi-dimensional search trees (extended abstract). In: Mehlhorn, K. (eds) STACS 85. STACS 1985. Lecture Notes in Computer Science, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024024
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DOI: https://doi.org/10.1007/BFb0024024
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