Optimal Online and Offline Algorithms for Finding Longest and Shortest Subsequences with Length and Sum Constraints

Sung Kwon KIM

doi:10.1587/transinf.E93.D.250

IEICE Transactions on Information and Systems

Online ISSN : 1745-1361
Print ISSN : 0916-8532

Special Section on Foundations of Computer Science

Optimal Online and Offline Algorithms for Finding Longest and Shortest Subsequences with Length and Sum Constraints

Sung Kwon KIM

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Keywords: length constraint, longest subsequence, offline algorithm, online algorithm, shortest subsequence, sum constraint

JOURNAL FREE ACCESS

2010 Volume E93.D Issue 2 Pages 250-256

DOI https://doi.org/10.1587/transinf.E93.D.250

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Abstract

In this paper, we address the following problems: Given a sequence A of n real numbers, and four parameters I, J, X and Y with I ≤ J and X ≤ Y, find the longest (or shortest) subsequence of A such that its length is between I and J and its sum is between X and Y. We present an online and an offline algorithm for the problems, both run in O(n log n) time, which are optimal.

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