Optimal algorithms for complete linkage clustering in d dimensions

Authors:
Drago Krznaric;Christos Levcopoulos
Affiliations:
Department of Computer Science, Lund University, Box 118, S-221 00 Lund, Sweden;Department of Computer Science, Lund University, Box 118, S-221 00 Lund, Sweden
Venue:
Theoretical Computer Science
Year:
2002

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Abstract

It is shown that the complete linkage clustering of n points in Rd, where d ≥ 1 is a constant, can be computed in optimal O(nlogn) time and linear space, under the L1 and L∞-metrics. Furthermore, for every other fixed Lt-metric, it is shown that it can be approximated within an arbitrarily small constant factor in O(nlogn) time and linear space.