Algorithms for the maximum subarray problem based on matrix multiplication
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Programming pearls: perspective on performance
Communications of the ACM
Programming pearls: algorithm design techniques
Communications of the ACM
A Linear Time Algorithm for Finding All Maximal Scoring Subsequences
Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology
Improved algorithms for the K-maximum subarray problem for small K
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Improved algorithms for the k maximum-sums problems
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Efficient algorithms for k maximum sums
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A sub-cubic time algorithm for the k-maximum subarray problem
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
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The maximum subarray problem is to find the array portion that maximizes the sum of array elements in it. For K disjoint maximum subarrays, Ruzzo and Tompa gave an O(n) time solution for one-dimension. This solution is, however, difficult to extend to two-dimensions. While a trivial solution of O(Kn3) time is easily obtainable for two-dimensions, little study has been undertaken to better this. We first propose an O(n+Klog K) time solution for one-dimension. This is equivalent to Ruzzo and Tompa’s when order is considered. Based on this, we achieve O(n3+Kn2log n) time for two-dimensions. This is cubic time when K≤ n/log n.