TY - GEN

T1 - How to search in history

AU - Chazelle, Bernard

N1 - Publisher Copyright:
© 1983, Springer-Verlag.

PY - 1983

Y1 - 1983

N2 - 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.

AB - 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.

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U2 - 10.1007/3-540-12689-9_93

DO - 10.1007/3-540-12689-9_93

M3 - Conference contribution

AN - SCOPUS:84944984120

SN - 9783540126898

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 52

EP - 63

BT - Foundations of Computation Theory - Proceedings of the 1983 International FCT-Conference

A2 - Karpinski, Marek

PB - Springer Verlag

T2 - International Symposium on Fundamentals of Computation Theory, FCT 1983

Y2 - 21 August 1983 through 27 August 1983

ER -