The overreaching topic of this dissertation is the adaptation of complex algorithms, which are extensively used in industrial applications, to the requirements dictated by the Big Data needs. Chosen algorithms are adapted to a distributed environment and made suitable for large amounts of data in such a way, that the increasing problem size can be compensated with scaling of the computing environment. Here is the emphasis particularly on horizontal scaling, i.e. the increase of the number of distributed computing units.The following problems are considered:1. The power flow problem in a smart grid system2. The contingency analysis problem in a smart grid system3. The spectral sparsification problem of graphs in the broader senseThe results indicate a reasonable execution time achieved by open-source software that is easily scalable and serve to direct further research in overcoming the current limitations.In a broader sense, although these problems seem very specific in their domain of application, the underlying core mechanics contain common mathematical challenges, applicable to a broad spectrum of problems.