This report aimed to develop algorithms for solving the optimization problem of matchingbuy and sell orders in call auctions while minimizing the number of transactions. The developed algorithms were evaluated based on their execution time and solution accuracy.The study found that the problem was more difficult to solve than initially anticipated, and commercial solvers were inadequate for the task. The data’s characteristics werecritical to the algorithms’ performance, and the lack of specifications for instruments andexchange posed a challenge. The algorithms were tested on a broad range of datasets with different characteristics, as well as real trades of stocks from the Stockholm Stock Exchange. Evaluating the best-performing algorithm became a trade-off between time and accuracy, where the quickest algorithm did not have the highest solution accuracy. Therefore, the importance of these factors should be considered before deciding which algorithm to implement. Eight algorithms were evaluated: four greedy algorithms and four clusteralgorithms capable of identifying 2-1 and 3-1 matches. If execution time is the single most crucial factor, the Unsorted Greedy Algorithm should be considered. However, if accuracyi s a priority, the Cluster 3-1 & 1-3 Algorithm should be considered, even though it takes longer to find a solution. Ultimately, the report concluded that while no single algorithm can be definitively la-beled as the best, the Cluster 2-1 Algorithm strikes the most effective balance between execution time and solution accuracy, while also remaining relatively stable in perfor-mance for all test cases. The recommendation was based on the fact that the Cluster 2-1 Algorithm proved to be the quickest of the developed cluster algorithms, and that cluster algorithms were able to find the best solutions for all tested data sets. This study successfully addressed its purpose by developing eight algorithms that solved the given problem and suggested an appropriate algorithm that strikes a balance between execution time and solution quality.

В работе рассмотрены разбиения целых неотрицательных чисел и изучены некоторые детали строения решеток разбиений. Решетка разбиений задается отношением доминирования, которое определяется как покомпонентное доминирование соответственных частичных сумм разбиений. Особое внимание уделено графическим разбиениям. Графическим называется разбиение, которые составлено из степеней вершин графа с добавлением нулей. Проведено исследование множества максимальных графических разбиений, доминирующих заданное графическое разбиение. Для исследования написана компьютерная программа на языке Python, позволяющая проверять гипотезы для разбиений небольших чисел. Основной результат работы – алгоритм построения всех максимальных графических разбиений, доминирующих заданное разбиение и имеющих такой же вес. Этот алгоритм базируется на основной теореме, которая описывает точное строение множества таких максимальных графических разбиений. Приведена программная реализация найденного алгоритма. / The work examines partitions of non-negative integers and studies some details of the structure of partition lattices. The lattice of partitions is given by a dominance relation, which is defined as the component-wise dominance of the corresponding partial sums of partitions. Particular attention is paid to graphical divisions. A graphical partition is a partition that is composed of the degrees of the vertices of the graph with the addition of zeros. A study of the set of maximal graphical partitions that dominate a given graphical partition has been carried out. For the study, a computer program was written in Python, which allows testing hypotheses for partitions of small numbers. The main result of the work is an algorithm for constructing all maximal graphical partitions that dominate a given partition and have the same weight. This algorithm is based on a fundamental theorem that describes the exact structure of the set of such maximal graphical partitions. A software implementation of the found algorithm is given.