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

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).

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