Abstract:
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This paper introduces randomized K-dimensional binary search trees
(randomized Kd-trees), a variant of K-dimensional binary trees. This
data structure allows the efficient maintenance of multidimensional
records for any sequence of insertions and deletions; and thus, is
fully dynamic. We show that several types of associative queries are
efficiently supported by randomized Kd-trees. In particular, a
randomized Kd-tree with n records answers exact match queries in
expected O(log n) time. Partial match queries are answered in
expected O(n^{1-f(s/K)}) time, when s out of K attributes
are specified, with 0 < f(s/K) < 1 a real valued function of s/K.
Nearest neighbor queries are answered on-line in expected O(log n) time.
Our randomized algorithms guarantee that their expected
time bounds hold irrespective of the order and number of insertions
and deletions. |