How to search in history

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 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. This scheme requires O(n + h) space and O(log n log h) query response-time, which saves a factor of log n space over previous structures. Aside from its improved performance, the novelty of our 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 our method makes it useful to a number of problems in three-dimensional geometry. For example, we are able to give fast algorithms for locating a point in a 3d-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 only O(n2) preprocessing, we can determine in O(log2 n) time which of n given points in E3 is closest to an arbitrary query point.

Original languageEnglish (US)
Title of host publicationFoundations of Computation Theory - Proceedings of the 1983 International FCT-Conference
EditorsMarek Karpinski
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540126898
StatePublished - 1983
Externally publishedYes
EventInternational Symposium on Fundamentals of Computation Theory, FCT 1983 - Borgholm, Sweden
Duration: Aug 21 1983Aug 27 1983

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume158 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


OtherInternational Symposium on Fundamentals of Computation Theory, FCT 1983

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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