Improved algorithms for the K overlapping maximum convex sum problem

Thaher, Mohammed; Takaoka, Tadao

doi:10.1016/j.procs.2012.04.081

Cited by 5 publications

(7 citation statements)

References 23 publications

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“…Using the convex shape approach accurately determines the peaks of data by optimising the sums. This study extends our earlier publications [12,13,14] with the addition of a potential application for the K-DMCSP.…”

Section: Motivation For Using the K-dmcspsupporting

confidence: 86%

“…Traditionally, maximum sub-arrays in a matrix are identified as rectangular regions that include elements which return the largest possible sum. As an alternative to the rectangular shape for selecting the promising portion of the matrix, the convex shape approach has been proposed [12][13][14]. This provides a maximised gain compared to that obtained from the rectangular shape.…”

Section: Review Of the K-dmsamentioning

confidence: 99%

“…Other research called the shape a rectilinear convex shape [16]. In this study we will use the concept of the convex shape, which is not following the geometrical convex shape definition [12,14]. The convex shape combines two with a top contour inclining or remaining horizontal and a bottom contour declining or remaining flat from left to right [12], whereas the N Shape is a mirror image of the W [12,14].…”

Section: Our Approach the K-k K Dmcspmentioning

confidence: 99%

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Application of the Maximum Convex Sum Algorithm in Determining Environmental Variables that Affect Nigerian Highland Stream Benthic Communities

Thaher

Umar

Takaoka

et al. 2013

Procedia Computer Science

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In this paper, we utilise the newly developed method K-Disjoint Maximum Convex Sum Problem (K-DMCSP) in a real-life application, which investigates the effects of land use changes on benthic stream communities in highland tropical streams of Nigeria. A collaboration between computer scientists and freshwater biologists was established to implement and examine the robustness of this approach compared to a traditional method that used rectangular shape in the K-Disjoint Maximum Sub-Array algorithm (K-DMSA). This novel approach uses the K-DMCSP, which utilises a convex shape as compared to a rectangular shape. In the above comparison the new approach using the convex shape optimises the sum and yields more accurate and precise results. This is because using the rectangular shape is limiting and is therefore not flexible enough to cover various sets of data distributions. The new approach was applied to data that were collated from 55 tropical highland streams on the Mambilla Plateau, Nigeria to investigate the interactions between substrate index or dissolved oxygen and temperature with number of macroinvertebrates (taxa). The K-DMCSP method located the K-maximum threshold values. This was achieved by defining the substrate index or dissolved oxygen associated most with the temperature by maximising the sum of elements of a selected portion of a two dimensional array. The K-DMCSP successfully detected the various temperatures between the different categories of the substrate index or dissolved oxygen, and how those variables affect numbers of macroinvertebrates. Furthermore, applying the algorithm revealed that the number of macroinvertebrates differs according to land use (e.g. forestry and agriculture). The new method used in this paper is encouraging in its capability to find the relationship between various environmental parameters and macroinvertebrate distribution and diversity. This method can potentially be applied to other real-life applications requiring finding associations between different parameters. .

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Section: Motivation For Using the K-dmcspsupporting

confidence: 86%

Section: Review Of the K-dmsamentioning

confidence: 99%

Section: Our Approach the K-k K Dmcspmentioning

confidence: 99%

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Application of the Maximum Convex Sum Algorithm in Determining Environmental Variables that Affect Nigerian Highland Stream Benthic Communities

Thaher

Umar

Takaoka

et al. 2013

Procedia Computer Science

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“…For practical purposes, we sometimes need the shape itself. This problem was solved by Thaher [13] for the sequential algorithm (Algorithm 11). We show how the idea works in our parallel situation.…”

Section: Computation Of the Boundarymentioning

confidence: 99%

Efficient Algorithms for the Maximum Sum Problems

Bae¹,

Shinn²,

Takaoka

2017

Algorithms

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Abstract:We present efficient sequential and parallel algorithms for the maximum sum (MS) problem, which is to maximize the sum of some shape in the data array. We deal with two MS problems; the maximum subarray (MSA) problem and the maximum convex sum (MCS) problem. In the MSA problem, we find a rectangular part within the given data array that maximizes the sum in it. The MCS problem is to find a convex shape rather than a rectangular shape that maximizes the sum. Thus, MCS is a generalization of MSA. For the MSA problem, O(n) time parallel algorithms are already known on an (n, n) 2D array of processors. We improve the communication steps from 2n − 1 to n, which is optimal. For the MCS problem, we achieve the asymptotic time bound of O(n) on an (n, n) 2D array of processors. We provide rigorous proofs for the correctness of our parallel algorithm based on Hoare logic and also provide some experimental results of our algorithm that are gathered from the Blue Gene/P super computer. Furthermore, we briefly describe how to compute the actual shape of the maximum convex sum.

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“…The convex shape is a more flexible shape to cover various data distribution. The convex shape is defined as a shape that has a centre column linked with"W" and "N" shapes; such a column is called an anchor column, [12][13][14] as shown in Figure 6. Other researchers call the shape a rectilinear convex shape.…”

Section: Maximum Convex Sum Problemmentioning

confidence: 99%

Maximum subarray algorithms for use in astronomical imaging

Weddell¹,

Read²,

Thaher³

et al. 2013

J. Electron. Imaging

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The maximum subarray problem is used to identify the subarray of a two dimensional array, where the sum of elements is maximized. In terms of image processing, the solution has been used to find the brightest region within an image. Two parallel algorithms of the maximum subarray problem solve this problem in O(n) and O(log n) time. A field programmable gate array implementation has verified theoretical maximum performance, however extensive customisation is required restricting general application. A more convenient platform for this work is a graphics processor unit, since it offers a flexible trade-off between hardware customization and performance. Implementation of the maximum subarray algorithm on a graphics processor unit is discussed in this article for rectangular solutions and convex extensions are explored.

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Improved algorithms for the K overlapping maximum convex sum problem

Cited by 5 publications

References 23 publications

Application of the Maximum Convex Sum Algorithm in Determining Environmental Variables that Affect Nigerian Highland Stream Benthic Communities

Application of the Maximum Convex Sum Algorithm in Determining Environmental Variables that Affect Nigerian Highland Stream Benthic Communities

Efficient Algorithms for the Maximum Sum Problems

Maximum subarray algorithms for use in astronomical imaging

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