Efficient Algorithms for k Maximum Sums

We study the problem of computing the k maximum sum subsequences. Given a sequence of real numbers x1, x2, . . . , xn and an integer parameter k, 1 k 1 2 n(n - 1), the problem involves finding the k largest values of j =i x for 1 i j n. The problem for fixed k = 1, also known as the maximum sum subsequence problem, has received much attention in the literature and is linear-time solvable. Recently, Bae and Takaoka presented a (nk)-time algorithm for the k maximum sum subsequences problem. In this paper we design an efficient algorithm that solves the above problem in O(min{k +n log2 n, n k}) time in the worst case. Our algorithm is optimal for k = (n log2 n) and improves over the previously best known result for any

• Type: Journal
• Year: 2006
• Where: ALGORITHMICA
• Authors: Fredrik Bengtsson, Jingsen Chen
• Keywords: ALGORITHMICA 2006, Maximum Sum Subsequence, Real Numbers, Sum Subsequence Problem