Contemporary P2P networks bring very high demands to the network infrastructure for video transmission. In the article, the problem of the optimal distribution of data streams is considered in the peer-to-peer networks for transmitting the television channels. There are various schemes for organizing the structure of an overlaid P2P system, which are used to improve the quality of television broadcasting services. In the work, the discrete multi-criteria formulation of this problem is proposed. Three sets are defined: a collection of viewers, a set of channels for viewing, and a set of streams, into which the channels can distribute. Each user watches a canal and several streams assigned to transfer. As a result, the system performance improves this thread assignment. For example, switching between the channels reduces the transmitting time. The mathematical model is described in the language of the hypergraph theory in 3 criteria recipe. The hypergraph edge weights: playback start time, interruption time, and several lost packets. The first two criteria have the MINMAX form, and the third criterion is of the MINSUM form. Using these criteria allows you to take simultaneously into account the start time of the video, the time when the playback was interrupted, and the number of data packets lost during the transmission. © 2020 American Institute of Physics Inc.. All rights reserved.