A new upper bound on the complexity of the all pairs shortest path problem
Information Processing Letters
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
Improved algorithm for all pairs shortest paths
Information Processing Letters
Improved Algorithms for the K-Maximum Subarray Problem
The Computer Journal
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An O(n3 (loglogn/logn)5/4) time algorithm for all pairs shortest paths
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
An O(n3loglogn/logn) time algorithm for the all-pairs shortest path problem
Information Processing Letters
Algorithm for K disjoint maximum subarrays
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Randomized algorithm for the sum selection problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Improved algorithms for the k maximum-sums problems
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
All-pairs shortest paths with real weights in O(n3/ log n) time
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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
A linear time algorithm for the k maximal sums problem
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Effect of corner information in simultaneous placement of K rectangles and tableaux
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
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We design a faster algorithm for the k-maximum subarray problem under the conventional RAM model, based on distance matrix multiplication (DMM). Specifically we achieve O(n3 √log log n/ log n + k log n) for a general problem where overlapping is allowed for solution arrays. This complexity is sub-cubic when k = o(n3/ log n). The best known complexities of this problem are O(n3 + k log n), which is cubic when k = O(n3/ log n), and O(kn3 √log log n/ log n), which is sub-cubic when k = o(√log n/ log log n).