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- W1584851036 abstract "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 $O({rm min}{k+n{rm log}^{2}n,nsqrt{k}})$ -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(n 2d − 1 + k logmin{n, k})–time algorithm for the d-dimensional version of the problem, where d>1 and each dimension, without loss of generality, is of the same size n. This improves the best previously known O(n 2d − 1 C)-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 $O({{m^{2}n} over {{rm log} n }})$ ." @default.
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- W1584851036 date "2005-01-01" @default.
- W1584851036 modified "2023-10-17" @default.
- W1584851036 title "Improved Algorithms for the k Maximum-Sums Problems" @default.
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- W1584851036 doi "https://doi.org/10.1007/11602613_80" @default.
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