Data mining using two-dimensional optimized association rules: scheme, algorithms, and visualization
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
Algorithms for the maximum subarray problem based on matrix multiplication
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Programming pearls: algorithm design techniques
Communications of the ACM
Journal of Computer and System Sciences - Computational biology 2002
A Linear Time Algorithm for Finding All Maximal Scoring Subsequences
Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology
An optimal algorithm for maximum-sum segment and its application in bioinformatics
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
Efficient algorithms for k maximum sums
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
On the range maximum-sum segment query problem
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Fast algorithms for finding disjoint subsequences with extremal densities
Pattern Recognition
Theoretical Computer Science
A sub-cubic time algorithm for the k-maximum subarray problem
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Algorithm for K disjoint maximum subarrays
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Efficient algorithms for the sum selection problem and k maximum sums problem
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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Given a sequence of n real numbers and an integer k, $1 \leq k \leq {1 \over 2}n(n - 1)$, the k maximum-sum segments problem is to locate the k segments whose sums are the k largest among all possible segment sums. Recently, Bengtsson and Chen gave an $O({\rm min}\{k+n{\rm log}^{2}n,n\sqrt{k}\})$-time algorithm for this problem. In this paper, we propose an O(n+k log(min{n, k}))-time algorithm for the same problem which is superior to Bengtsson and Chen's when k is o(nlog n). We also give the first optimal algorithm for delivering the k maximum-sum segments in non-decreasing order if k ≤ n. Then we develop an O(n2d−1+k logmin{n, k})–time algorithm for the d-dimensional version of the problem, where d1 and each dimension, without loss of generality, is of the same size n. This improves the best previously known O(n2d−1C)-time algorithm, also by Bengtsson and Chen, where $C = {\rm min}\{k + n {\rm log}^{2} n, n{\sqrt{k}}\}$. It should be pointed out that, given a two-dimensional array of size m × n, our algorithm for finding the k maximum-sum subarrays is the first one achieving cubic time provided that k is $O({{m^{2}n} \over {{\rm log} n }})$.