Search Algorithms for a System of Different Representatives of Subsets of a Finite Set

The paper considers various aspects and approaches regarding the search for a system of differenrt representatives (SDR) of subsets of a finite set. Algorithm 3 has been developed, which is an algorithmization of the search process for SDR on the basis of Hall's theorem on the existence of SDR. Algorithms 1-5 for searching for partial and complete SDRs based on the technology for solving problems of the transport type, in particular, the algorithm associated with the construction of cycles, are given. SDR search algorithms can be used as auxiliary tools for solving combinatorial problems. It is also shown, conversely, that the search for SDR can be considered as a combinatorial optimization problem. Mathematics Subject Classification – MSC2020: 90-08, 90B06, 90C27