A note on ranking k maximum sums

In this paper, we design a fast algorithm for ranking the k maximum sum subsequences. Given a sequence of real numbers 〈x1, x2, · · · , xn 〉 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