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The Computer Journal 2006 49(3):358-374; doi:10.1093/comjnl/bxl007
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© The Author 2006. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Improved Algorithms for the K-Maximum Subarray Problem

Sung Eun Bae* and Tadao Takaoka

Department of Computer Science and Software Engineering, University of Canterbury Christchurch, New Zealand

*Corresponding author: seb43{at}student.canterbury.ac.nz

The maximum subarray problem is to find the contiguous array elements having the largest possible sum. We extend this problem to find K maximum subarrays. For general K maximum subarrays where overlapping is allowed, Bengtsson and Chen presented Formula time algorithm for one-dimensional case, which finds unsorted subarrays. Our algorithm finds K maximum subarrays in sorted order with improved complexity of O ((n + K) log K). For the two-dimensional case, we introduce two techniques that establish O(n3) and subcubic time.

Key Words: Maximum subarray • persistent 2-3 tree • selection in matrices with sorted columns • distance matrix multiplication


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