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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.

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. .