Abstract: The present invention is a computer system and associated method configured to in support of solving NP-complete problems such as minimal Hamiltonian cycle type problems. According to the invention, a primary network represented by the matrix of its edges is recorded in the memory space, and an equivalent representation of the primary network is formed as a set of subnetworks. Nodes of a present path are reordered according to a set of reordering rules and edge weights of edges of the set of subnetworks are changed according to a set of edge weight changing rules.