Adding range restriction capability to dynamic data structures

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 <italic>n</italic> elements, provided that the problem satisfies a certain decomposability condition and that one is willing to allow increases by a factor of <italic>O</italic>(log <italic>n</italic>) 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 <italic>k</italic> dimensions with worst-case times of <italic>O</italic>(log<italic><supscrpt>k</supscrpt> n</italic>) for each insertion, deletion, or query operation.

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