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(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).

• Type: Conference
• Year: 2007
• Where: ISAAC
• Authors: Sung Eun Bae, Tadao Takaoka
• Keywords: ISAAC 2007, Log N, Log N/, N/ Log