It is a quite common situation when some practical problems are reduced to solving systems of linear equations. If in these equations systems the number of variables is relatively small, then their solving is done quite efficiently and there are no problems regarding the memory of the computing system and regarding the problem speed calculation. When solving problems with a large number of unknowns these problems persist. In order to reduce the required amount of memory, the matrix of coefficients of the system of linear equations is required to be presented in a“good”, convenient form, for example in triangular form, in band form, in block form, etc. The problems of transforming a matrix to a band-type matrix of minimum width usually reduce to a problem of renumbering the vertices of a graph whose incidence matrix is obtained from the original matrix and two vertices u; v of the graph are adjacent if and only if element auv is non-zero. It is clear that this procedure uniquely matches each matrix with a graph G = (V;E). In 1976 it was demonstrated [1], that if the graph is arbitrary, then the problem of determining the minimum width of the band is NP-complete. In 1978 it was demonstrated [2], that the above-mentioned problem is also NPcomplete for trees with vertex valence lower than three. Based on the above, it is clear that it would be reasonable to develop approximate algorithms for solving the problem. Currently, several approximate algorithms are known for solving the problem of finding the minimum bandwidth, the most frequently used being the CuthillaMcKee algorithm, published by the authors in 1969. An algorithm of the same type is presented in this paper. At the origin of the algorithm is the following observation: if y is a vertex already numbered, and z is an unnumbered neighbor of y, then in order to reduce the bandwidth, the line corresponding to z it will be assigned a number, which was not used and which is closer to y.

It is a quite common situation when some practical problems are reduced to solving systems of linear equations. If in these equations systems the number of variables is relatively small, then their solving is done quite efficiently and there are no problems regarding the memory of the computing system and regarding the problem speed calculation. When solving problems with a large number of unknowns these problems persist. In order to reduce the required amount of memory, the matrix of coefficients of the system of linear equations is required to be presented in a“good”, convenient form, for example in triangular form, in band form, in block form, etc. The problems of transforming a matrix to a band-type matrix of minimum width usually reduce to a problem of renumbering the vertices of a graph whose incidence matrix is obtained from the original matrix and two vertices u; v of the graph are adjacent if and only if element auv is non-zero. It is clear that this procedure uniquely matches each matrix with a graph G = (V;E). In 1976 it was demonstrated [1], that if the graph is arbitrary, then the problem of determining the minimum width of the band is NP-complete. In 1978 it was demonstrated [2], that the above-mentioned problem is also NPcomplete for trees with vertex valence lower than three. Based on the above, it is clear that it would be reasonable to develop approximate algorithms for solving the problem. Currently, several approximate algorithms are known for solving the problem of finding the minimum bandwidth, the most frequently used being the CuthillaMcKee algorithm, published by the authors in 1969. An algorithm of the same type is presented in this paper. At the origin of the algorithm is the following observation: if y is a vertex already numbered, and z is an unnumbered neighbor of y, then in order to reduce the bandwidth, the line corresponding to z it will be assigned a number, which was not used and which is closer to y.