Adding range restriction capability to dynamic data structures

Authors:
Dan E. Willard;George S. Lueker
Affiliations:
State Univ. of New York at Albany, Albany/ and Bell Communications Research;Univ. of California at Irvine, Irvine
Venue:
Journal of the ACM (JACM)
Year:
1985

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Abstract

A database is said to allow range restrictions if one may request that only records with some specified field in a specified range be considered when answering a given query. A transformation is presented that enables range restrictions to be added to an arbitrary dynamic data structure on n elements, provided that the problem satisfies a certain decomposability condition and that one is willing to allow increases by a factor of O(log n) in the worst-case time for an operation and in the space used. This is a generalization of a known transformation that works for static structures. This transformation is then used to produce a data structure for range queries in k dimensions with worst-case times of O(logk n) for each insertion, deletion, or query operation.