An algorithm for a generalized maximum subsequence problem

Authors:
Thorsten Bernholt;Thomas Hofmeister
Affiliations:
Informatik 2, Universität Dortmund, Dortmund, Germany;Informatik 2, Universität Dortmund, Dortmund, Germany
Venue:
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Year:
2006

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Abstract

We consider a generalization of the maximum subsequence problem. Given an array a1,...,an of real numbers, the generalized problem consists in finding an interval [i,j] such that the length and the sum of the subsequence ai,...,aj maximize a given quasiconvex function f. Problems of this type occur, e.g., in bioinformatics. We show that the generalized problem can be solved in time O(n log n). As an example, we show how the so-called multiresolution criteria problem can be solved in time O(n log n).