On the range maximum-sum segment query problem

Authors:
Kuan-Yu Chen;Kun-Mao Chao
Affiliations:
Department of Computer Science and Information Engineering, Institute of Networking and Multimedia, National Taiwan University, Taipei, Taiwan;Department of Computer Science and Information Engineering, Institute of Networking and Multimedia, National Taiwan University, Taipei, Taiwan
Venue:
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Year:
2004

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Abstract

We are given a sequence A of n real numbers which is to be preprocessed In the Range Maximum-Sum Segment Query (RMSQ) problem, a query is comprised of two intervals [i,j] and [k,l] and our goal is to return the maximum-sum segment of A whose starting index lies in [i,j] and ending index lies in [k,l] We propose the first known algorithm for this problem in O(n) preprocessing time and O(1) time per query under the unit-cost RAM model We also use the RMSQ techniques to solve three relevant problems in linear time These variations on the basic theme demonstrate the utilities of the techniques developed in this paper.