Supercomputers and Discrete Topology

Abstract

For simulation of objects of discrete topology, supercomputers are often used. This can be explained by the combinatorial nature of the problems examined, especially in the study of the dynamics of rearrangements of such structures. In this paper, we consider three methods of coding associated with the parallelization of computations: (1) coding of cubic complexes; (2) coding for the calculation of transition probabilities in Markov chains in the reconstructions of triangulations of Euclidean spaces; (3) coding of topological situations in the transformations of complexes, i.e., discrete analogs of homotopic transformation. The base chosen for the geometric and topological objects possesses “minimal” mathematical resources (integer points and primitive vectors in Euclidean spaces).