The longest almost-increasing subsequence

Authors:
Amr Elmasry
Affiliations:
Max-Planck Institut für Informatik, Saarbrücken, Germany
Venue:
Information Processing Letters
Year:
2010

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Abstract

Given a sequence of n elements, we introduce the notion of an almost-increasing subsequence as the longest subsequence that can be converted to an increasing subsequence by possibly adding a value, that is at most a fixed constant, to each of the elements. We show how to optimally construct such subsequence in O(nlogk) time, where k is the length of the output subsequence.