Improved Algorithms for the K-Maximum Subarray Problem

Themaximum subarray problem is to find the contiguous array elements having the largest possible sum. We extend this problem to find K maximum subarrays. For general K maximum subarrays where overlapping is allowed, Bengtsson and Chen presented OðminfK + n logn‚ n ffiffiffiffi K p gÞ time algorithm for one-dimensional case, which finds unsorted subarrays. Our algorithm finds K maximum subarrays in sorted order with improved complexity of O ((n + K ) logK ). For the twodimensional case, we introduce two techniques that establish O(n) and subcubic time.