Improved Algorithms for the K-Maximum Subarray Problem for Small K

The maximum subarray problem for a one- or two-dimensional array is to find the array portion that maiximizes the sum of array elements in it. The K-maximum subarray problem is to find the K subarrays with largest sums. We improve the time complexity for the one-dimensional case from O(min{K + n log2 n, n √ K}) for 0 ≤ K ≤ n(n − 1)/2 to O(n log K + K2 ) for K ≤ n. The latter is better when K ≤ √ n log n. If we simply extend this result to the two-dimensional case, we will have the complexity of O(n3 log K +K2 n2 ). We improve this complexity to O(n3 ) for K ≤ √ n.

• Type: Conference
• Year: 2005
• Where: COCOON
• Authors: Sung Eun Bae, Tadao Takaoka
• Keywords: COCOON 2005, Maximum Subarray Problem, Subarray Problem, Two-dimensional Array