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ON COMPUTING THE LENGTH OF LONGEST INCREASING SUBSEQUENCES
ON COMPUTING THE LENGTH OF LONGEST
INCREASING SUBSEQUENCES

Michael L. FREDMAN

Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, Mass. 02139, USA

Received 14 Match 1974
Revised 4 June 1974

Let S = x1, x2, ..., xn be a sequence of n distinct elements from a linearly ordered set. We consider the problem of determining the length of the longest increasing subsequences of S. An algorithm which performs this task is described and is shown to perform n log n - n log log n + O(n) comparisons in its worst case. This worst case behavior is shown to be best possible.
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