Two problems of weighted graphs approximation and their solution algorithms

Two approximation problems for weighted sparse graphs are considered. By the approximation error is meant the absolute value of the difference of the distances between the vertices in graph and the corresponding vertices in an approximation graph. The first problem is to minimize the approximation error under a given dimension of the approximation graph. The second problem is to minimize the dimension of the approximation graph under a given approximation error threshold. For both problems, their solution algorithms are proposed and their presentation in the form of a graph partitioning problem are presented.