A note on ranking k maximum sums
Fredrik Bengtsson, Jingsen Chen · 2005
In this paper, we design a fast algorithm for ranking the k maximum sum subsequences. Given a sequence of real numbers and an integer parameter k, the problem is to compute k subsequences of consecutive elements with the sums of their elements being the largest, second largest, ..., and the k:th largest among all possible range sums. For any value of k, 1 <= k <= n(n+1)/2, our algorithm takes O(n + k log n) time in the worst case to rank all such subsequences. Our algorithm is optimal for k <= n.