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Improved algorithms for the kmaximum subarray problem for small k
 In Proceedings of the 11th Annual International Conference on Computing and Combinatorics, volume 3595 of LNCS
, 2005
"... Abstract. The maximum subarray problem for a one or twodimensional array is to find the array portion that maiximizes the sum of array elements in it. The Kmaximum subarray problem is to find the K subarrays with largest sums. We improve the time complexity for the onedimensional case from O(min ..."
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Cited by 15 (5 self)
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Abstract. The maximum subarray problem for a one or twodimensional array is to find the array portion that maiximizes the sum of array elements in it. The Kmaximum subarray problem is to find the K subarrays with largest sums. We improve the time complexity for the onedimensional case from O(min{K + n log 2 n, n √ K}) for 0 ≤ K ≤ n(n − 1)/2 to O(n log K + K 2) for K ≤ n. The latter is better when K ≤ √ n log n. If we simply extend this result to the twodimensional case, we will have the complexity of O(n 3 log K + K 2 n 2).We improve this complexity to O(n 3) for K ≤ √ n. 1
Parallel Maximum Sum Algorithms on Interconnection Networks
 Queen’s Uni. Dept. of Com. and
, 1999
"... We develop parallel algorithms for both onedimensional and twodimensional versions of the maximum sum problem (or max sum for short) on several interconnection networks. These algorithms are all based on a simple scheme that uses prefix sums. To this end, we first show how to compute prefix sums o ..."
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Cited by 6 (0 self)
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We develop parallel algorithms for both onedimensional and twodimensional versions of the maximum sum problem (or max sum for short) on several interconnection networks. These algorithms are all based on a simple scheme that uses prefix sums. To this end, we first show how to compute prefix sums of N elements on a hypercube, a star, and a pancake interconnection network of size p (where p N) in optimal time of O( N p + log p). For the problem of maximum subsequence sum, the 1D version of the max sum problem, we find an algorithm that computes the maximum sum of N elements on the aforementioned networks of size p, all with a running time of O( N p + log p), which is optimal in view of the trivial\Omega\Gamma N p + log p) lower bound. When p = O( N log N ), our algorithm computes the max sum in O(log N) time, resulting in an optimal cost of O(N ). This result also matches the performance of two previous algorithms that are designed to run on PRAM. Our 1D max sum algorithm can...
Contents lists available at ScienceDirect Information Processing Letters
"... www.elsevier.com/locate/ipl Optimal algorithms for the averageconstrained maximumsum segment problem ..."
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www.elsevier.com/locate/ipl Optimal algorithms for the averageconstrained maximumsum segment problem