Selecting Sums in Arrays

  • Gerth Stølting Brodal
  • Allan Grønlund Jørgensen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)

Abstract

In an array of n numbers each of the \(\binom{n}{2}+n\) contiguous subarrays define a sum. In this paper we focus on algorithms for selecting and reporting maximal sums from an array of numbers. First, we consider the problem of reporting k subarrays inducing the k largest sums among all subarrays of length at least l and at most u. For this problem we design an optimal O(n + k) time algorithm. Secondly, we consider the problem of selecting a subarray storing the k’th largest sum. For this problem we prove a time bound of Θ(n · max {1,log(k/n)}) by describing an algorithm with this running time and by proving a matching lower bound. Finally, we combine the ideas and obtain an O(n· max {1,log(k/n)}) time algorithm that selects a subarray storing the k’th largest sum among all subarrays of length at least l and at most u.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Allan Grønlund Jørgensen
    • 1
  1. 1.BRICS, MADALGO, Department of Computer ScienceUniversity of AarhusDenmark

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