A Sub-Cubic Time Algorithm for the K-Maximum Subarray Problem

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(n^3√(loglog n/log n) + klog 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(kn^3√(loglog n/log n)) , which is sub-cubic when k=o(√(log n/loglog n)) .