Optimal grouping of interrelated ordered objects

The paper is concerned with grouping of objects by using a matrix of their interrelation provided that the objects are ordered in a specified way and the grouping should not be in conflict with it. A method is described of an accurate solution to this problem with comparatively weak constraints in the form of the functional to be maximized. The method is of the dynamic programming kind and requires $(c_1n+c_2)N^2$ algorithmical operations where $N$ is the number of objects, $n$ is the number of groups while $c_1$ and $c_2$ are constants.