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A Reliable Randomized Algorithm for the Closest-Pair Problem

โœ Scribed by Martin Dietzfelbinger; Torben Hagerup; Jyrki Katajainen; Martti Penttonen

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
361 KB
Volume
25
Category
Article
ISSN
0196-6774

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โœฆ Synopsis

The following two computational problems are studied: Duplicate grouping: Assume that n items are given, each of which is labeled by an ร„ 4 integer key from the set 0, . . . , U y 1 . Store the items in an array of size n such that items with the same key occupy a contiguous segment of the array.

Closest pair: Assume that a multiset of n points in the d-dimensional Euclidean space is given, where d G 1 is a fixed integer. Each point is represented as a ร„ 4 ลฝ . d -tuple of integers in the range 0, . . . , U y 1 or of arbitrary real numbers . Find a closest pair, i.e., a pair of points whose distance is minimal over all such pairs.

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