Assignment of Tasks to Machines Under Data Replication with a Tie to Steiner Systems

In the paper a problem of assignment of tasks to machines is formulated and solved, where a criterion of data replication is used and a large size of data imposes additional constraints. This problem is met in practice when dealing with large genomic files or other types of vast data. The necessity of comparing all pairs of files within a big set of DNA sequencing results, which we collected, maintained, and analyzed within a national genomic project, brought us to the proposed results. This problem resembles that of generating a particular Steiner system, and a mechanism observed there is employed in one of our algorithms. Based on the problem complexity, we propose two heuristic algorithms, which work very well even for instances with tight constraints and a heterogeneous environment defined. In addition, we propose a simplified method, nevertheless capable of finding very good solutions and surpassing the algorithms in some special cases. The methods are validated in tests on a wide set of instances, where values of parameters reflect our real-world application and where their usefulness is proven.