Longest increasing subsequences in sliding windows

Authors:
Michael H. Albert;Alexander Golynski;Angèle M. Hamel;Alejandro López-Ortiz;S. Srinivasa Rao;Mohammad Ali Safari
Affiliations:
Department of Computer Science, University of Otago, Dunedin, New Zealand;School of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;Department of Physics and Computer Science, Wilfrid Laurier University, Waterloo, Ont., Canada N2L 3C5;School of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;School of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;School of Computer Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

We consider the problem of finding the longest increasing subsequence in a sliding window over a given sequence (LISW). We propose an output-sensitive data structure that solves this problem in time O(n log log n+OUTPUT) for a sequence of n elements. This data structure substantially improves over the naïve generalization of the longest increasing subsequence algorithm and in fact produces an output-sensitive optimal solution.