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A Sub-cubic Time Algorithm for the k -Maximum Subarray Problem

Author:
Sung Eun Bae  Tadao Takaoka  


Journal:
Lecture Notes in Computer Science


Issue Date:
2007


Abstract(summary):

We design a faster algorithm for the k-maximum sub-array problem under the conventional RAM model, based on distance matrix multiplication (DMM). Specifically we achieve O(n3脰{loglogn/logn} + klogn)O(n^3\sqrt{\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(n 3/logn). The best known complexities of this problem are O(n 3 + klogn), which is cubic when k = O(n 3/logn), and O(kn3脰{loglogn/logn})O(kn^3\sqrt{\log\log n/\log n}) , which is sub-cubic when k=o(脰{logn/loglogn})k=o(\sqrt{\log n/\log\log n}) .


Page:
751-762


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