We consider discrete optimization problems with Boolean variables and rarefied matrices of large dimensions. In some cases we manage to extract the quasi-block structure of the initial matrices. In particular, in this paper we have problems with the so-called block-stair and block-tree structures. Blocks in such problems have connecting variables with other blocks. We present the parallelization of such large problems on GRID systems, where problems for separate blocks are solved independently of one another, and the initial problems cannot be directly solved due to the unacceptably large time requirements.