Improved Algorithms for the K-Maximum Subarray Problem for Small K

Bae, Sung Eun; Takaoka, Tadao

doi:10.1007/11533719_63

Cited by 16 publications

(22 citation statements)

References 15 publications

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“…An improvement achieving O(n log K + K 2 ) time for small K is presented in the preliminary version of this paper [13]. This solution is better than the previous one when K ffiffi ffi n p log n and is O(n log K ) time when K ffiffiffiffiffiffiffiffiffiffiffiffiffi n log n p .…”

Section: Introductionmentioning

confidence: 87%

“…We describe a simple solution that decreases the number of candidates from Kn to K 2 . Note that K 2 is considered to be smaller than Kn due to the assumption K n. This solution is introduced in the preliminary paper [13] and provides a starting point for the further improved algorithm in Section 4.…”

Section: Finding K Maximum Sums In O(kn) Timementioning

confidence: 99%

“…Let us examine the time complexity within the 'while' loop at lines [13][14][15][16][17][18][19][20][21][22][23]. We separate the analysis when p ¼ 0 and p !…”

Section: Improved Algorithms For the K-maximum Subarray Problem 367mentioning

confidence: 99%

“…This solution is better than the previous one when K ffiffi ffi n p log n and is O(n log K ) time when K ffiffiffiffiffiffiffiffiffiffiffiffiffi n log n p . This paper reviews the preliminary work [13] and first presents O(n log K ) time solution for K n. The extra K 2 term from O(n log K + K 2 ) is removed using a partially persistent data structure [14] and an efficient selection For Permissions, please email: journals.permissions@oxfordjournals.org doi:10.1093/comjnl/bxl007 algorithm in matrices with sorted columns [15]. Since K may be theoretically as large as n(n + 1)/2, we extend this solution to show that the same framework can be used for any K up to K ¼ n(n + 1)/2 with a complexity of O ((n + K ) log K ).…”

Section: Introductionmentioning

confidence: 99%

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Improved Algorithms for the K-Maximum Subarray Problem

Bae

Takaoka

2005

The Computer Journal

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The maximum subarray problem is to find the contiguous array elements having the largest possible sum. We extend this problem to find K maximum subarrays. For general K maximum subarrays where overlapping is allowed, Bengtsson and Chen presented OðminfK + n log 2 n‚ n ffiffiffi ffi K p gÞ time algorithm for one-dimensional case, which finds unsorted subarrays. Our algorithm finds K maximum subarrays in sorted order with improved complexity of O ((n + K ) log K ). For the twodimensional case, we introduce two techniques that establish O(n 3 ) and subcubic time.

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Section: Introductionmentioning

confidence: 87%

Section: Finding K Maximum Sums In O(kn) Timementioning

confidence: 99%

“…Let us examine the time complexity within the 'while' loop at lines [13][14][15][16][17][18][19][20][21][22][23]. We separate the analysis when p ¼ 0 and p !…”

Section: Improved Algorithms For the K-maximum Subarray Problem 367mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improved Algorithms for the K-Maximum Subarray Problem

Bae

Takaoka

2005

The Computer Journal

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“…, n] and a positive number k, consist in locate the k segments whose sum are the k largest among all possible sums. The k Maximum Sum Segments was first presented by Bae and Takaoka (5) and, after different solutions emerged (5,6,7,10,22,50), was optimally solved by Brodal and Jørgensen (15) in O(n + k)…”

Section: Related Workmentioning

confidence: 99%

On the Lower Bound for the Maximum Consecutive Sub-Sums Problem

RONCALLA¹

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Preparation, characterization, and potential biomedical application of composite sponges based on collagen from silver carp skin

Chen

Huang

Guo

et al. 2014

J of Applied Polymer Sci

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To reuse fish processing waste for biomedical materials, collagen (Col) was extracted from silver carp skin, and Col–chitosan (Ch) composite sponges were prepared by a freeze‐drying method. The atomic force microscopy and electrophoresis results suggest the Col might have been type I. To obtain the optimum conditions for the manufacture of the Col–Ch sponges, the characteristics of sponges composed of different ratios of Col to Ch with different crosslinkers were evaluated. Scanning electron microscopy showed that the sponges had an interconnected network structure with porosity. Infrared spectroscopy demonstrated that intermolecular crosslinkages between Col and Ch occurred. The swelling measurements implied that all of the sponges could bind an 18‐ to 36‐fold amount of distilled water and still maintain their form and stability. When the ratio of Col to Ch was higher than 1:0.25, the swelling and degradation rate decreased with increasing Ch. Cell proliferation, hemolysis, and hemostasis assay indicated that the sponges exhibited noncytotoxicity, biocompatibility, nonhemolysis, and hemostatic efficacy. Overall, we concluded that the optimal ratio of Col and Ch for the sponges was 1:0.25, and glutaraldehyde crosslinking was more suitable than 1‐ethyl‐3‐(3‐dimethylaminopropyl) carbodiimide hydrochloride. These results demonstrate the potential application of silver carp skin Col–Ch sponges for tissue engineering and wound dressing in non‐weight‐bearing tissue. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40998.

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Improved Algorithms for the K-Maximum Subarray Problem for Small K

Cited by 16 publications

References 15 publications

Improved Algorithms for the K-Maximum Subarray Problem

Improved Algorithms for the K-Maximum Subarray Problem

On the Lower Bound for the Maximum Consecutive Sub-Sums Problem

Preparation, characterization, and potential biomedical application of composite sponges based on collagen from silver carp skin

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