A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
A constant update time finger search tree
Information Processing Letters
Fast parallel algorithms for the maximum sum problem
Parallel Computing
Algorithms for the maximum subarray problem based on matrix multiplication
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Finger search trees with constant insertion time
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Algorithms sequential & parallel: a unified approach
Algorithms sequential & parallel: a unified approach
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
The Computer Journal
Efficient algorithms for k maximum sums
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Improved algorithmms for the k maximum-sums problems
Theoretical Computer Science
Theoretical Computer Science
Proceedings of the 2007 ACM symposium on Applied computing
Optimal algorithms for the average-constrained maximum-sum segment problem
Information Processing Letters
Algorithm for K disjoint maximum subarrays
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Computing maximum-scoring segments in almost linear time
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
A linear time algorithm for the k maximal sums problem
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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The maximum subarray problem for a one- or two-dimensional array is to find the array portion that maiximizes the sum of array elements in it. The K-maximum subarray problem is to find the K subarrays with largest sums. We improve the time complexity for the one-dimensional case from $O(min\{K+n\log^2 n, n\sqrt{K}\})$ for 0 ≤ K ≤ n(n–1)/2 to O(nlog K + K2) for K ≤ n. The latter is better when $K \le \sqrt n\log n$. If we simply extend this result to the two-dimensional case, we will have the complexity of O(n3log K + K2n2). We improve this complexity to O(n3) for $K \le \sqrt{n}$.