How to search in history

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43 Scopus citations


This paper considers the problem of granting a dynamic data structure the capability of remembering the situation it held at previous times. We present a new scheme for recording a history of h updates over an ordered set S of n objects, which allows fast neighbor computation at any time in the history. The novelty of the method is to allow the set S to be only partially ordered with respect to queries and the time measure to be multi-dimensional. The generality of the method makes it useful for a number of problems in 3-dimensional geometry. For example, we are able to give fast algorithms for locating a point in a 3-dimensional complex, using linear space, or for finding which of n given points is closest to a query plane. Using a simpler, yet conceptually similar technique, we show that with O(n2) preprocessing, it is possible to determine in O(log2 n) time which of n given points in E3 is closest to an arbitrary query point.

Original languageEnglish (US)
Pages (from-to)77-99
Number of pages23
JournalInformation and Control
Issue number1-3
StatePublished - 1985
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Engineering


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