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A Data Structure for the Maximum-Sum Segment Problem with Offsets

Author Yoshifumi Sakai

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LIPIcs.CPM.2024.26.pdf
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Author Details

Yoshifumi Sakai
  • Graduate School of Agricultural Science, Tohoku University, Japan

Funding

This work was supported by JSPS KAKENHI Grant Number JP23K10975.

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Yoshifumi Sakai. A Data Structure for the Maximum-Sum Segment Problem with Offsets. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CPM.2024.26

Abstract

Consider a variant of the maximum-sum segment problem for a sequence X₀ of n real numbers, which asks an arbitrary contiguous subsequence of X_a that maximizes the sum of its elements for any given real number a, where X_a is the sequence obtained by subtracting a from each element in X₀. Although this problem can be solved in O(n) time from scratch for any given X₀ and a, appropriate data structures for X₀ could support efficient queries of the solution for arbitrary a. We propose an O(n log² n)-time, O(n)-space algorithm that takes X₀ as input and outputs such a data structure supporting O(log n)-time queries.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • algorithms
  • sequence of real numbers
  • maximum-sum segment

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