Randomized Algorithm for the Sum Selection Problem

Efficient algorithms for the sum selection problem and k maximum sums problem

“…Cheng et al [10] and Bae and Takaoka [5] recently gave an O(n +k log(min{n, k})) time algorithm and an O((n + k) log k) time algorithm respectively, which is superior to Bengtsson and Chen's when k is o(n log n), but both run in O(n 2 log n) time in the worst case. Lin and Lee [15] recently gave an expected O(n log n + k) time randomized algorithm based on a randomized algorithm which finds in expected O(n log n) time the segment whose sum is the kth smallest by using a random sampling technique, for any given positive integer 1 ≤ k ≤ n(n−1) 2 . The latter problem is referred to as the Sum Selection Problem.…”

Optimal algorithms for the average-constrained maximum-sum segment problem

“…Since then, there have been many variants proposed. The k MaximumSum Segments problem [3][4][5]10,12,18,19] is to locate the k segments whose sums are the k largest among all possible sums, and is solvable in O (n + k) time [10,21]. The Range Maximum-Sum Segment Query (RMSQ) problem is to preprocess the input sequence such that any range maximum-sum segment query can be answered quickly, where a range maximum-sum segment query specifies two intervals [i, j] and [k, l] and the goal is to find a segment A(x, y) with maximum sum subject to i x j and k y .…”

Efficient Algorithms for the Sum Selection Problem and K Maximum Sums Problem

“…Cheng et al [8] recently gave an O(n + k log(min{n, k})) time algorithm for this problem which is superior to Bengtsson and Chen's when k is o(n log n), but it runs in O(n 2 log n) time in the worst case. Lin and Lee [14] recently gave an expected O(n log n + k) time randomized algorithm based on a randomized algorithm which finds in expected O(n log n) time the segment whose sum is the k-th smallest, for any given pos-…”