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Optimal Online and Offline Algorithms for Finding Longest and Shortest Subsequences with Length and Sum Constraints
Sung Kwon KIM
IEICE TRANSACTIONS on Information and Systems
Publication Date: 2010/02/01
Online ISSN: 1745-1361
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science)
length constraint, longest subsequence, offline algorithm, online algorithm, shortest subsequence, sum constraint,
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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(nlog n) time, which are optimal.