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2 International Journal of Applied Mathematics and Computer Science

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Exact algorithms for the satellite image selection problem

Swat Sylwester, Antczak Maciej, Zok Tomasz, Blazewicz Jacek, Musial Jędrzej

International Journal of Applied Mathematics and Computer Science

2025

Vol. 35, no. 2

293--309

Space development is more relevant than ever with the increasing number of satellite launches for various applications. The amount of space data collected daily is growing exponentially and many customers are interested in continuously monitoring different regions of the Earth. It often requires stitching together many images from other providers to cover an Area of Interest (AOI), resulting in a mosaic. Each satellite image has various parameters, such as cost, download time, cloud coverage, and resolution. The main question is how to optimally select the subset of available images to fully cover the AOI while minimizing total cost and cloud coverage. The problem is known as satellite image mosaic selection (SIMS).Manual selection of promising images is often impossible, especially when dealing with large AOIs or many photos. To solve the problem, we propose several new exact algorithms using different techniques, such as branch-and-bound or mixed-integer linear programming. These algorithms show quality and efficiency compared with existing approaches and are expected to benefit various industrial applications.

New models and algorithms for RNA pseudoknot order assignment

Zok Tomasz, Badura Jan, Swat Sylwester, Figurski Kacper, Popenda Mariusz, Antczak Maciej

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 2

315--324

The pseudoknot is a specific motif of the RNA structure that highly influences the overall shape and stability of a molecule. It occurs when nucleotides of two disjoint single-stranded fragments of the same chain, separated by a helical fragment, interact with each other and form base pairs. Pseudoknots are characterized by great topological diversity, and their systematic description is still a challenge. In our previous work, we have introduced the pseudoknot order: a new coefficient representing the topological complexity of the pseudoknotted RNA structure. It is defined as the minimum number of base pair set decompositions, aimed to obtain the unknotted RNA structure. We have suggested how it can be useful in the interpretation and understanding of a hierarchy of RNA folding. However, it is not trivial to unambiguously identify pseudoknots and determine their orders in an RNA structure. Therefore, since the introduction of this coefficient, we have worked on the method to reliably assign pseudoknot orders in correspondence to the mechanisms that control the biological process leading to their formation in the molecule. Here, we introduce a novel graph coloring-based model for the problem of pseudoknot order assignment. We show a specialized heuristic operating on the proposed model and an alternative integer programming algorithm. The performance of both approaches is compared with that of state-of-the-art algorithms which so far have been most efficient in solving the problem in question. We summarize the results of computational experiments that evaluate our new methods in terms of classification quality on a representative data set originating from the non-redundant RNA 3D structure repository.