Polynomial algorithm for the path facility location problem with uniform capacities

The Facility Location Problem with uniform capacities on path graphs is considered. Earlier it was shown by Ageev that this problem can be solved in $O(m^3n^3+m^5n^2)$ time, where $m$ is the number of facilities and $n$ is the number of clients. In the paper the modified algorithm is presented that has reduced infinitesimal order for the time complexity $O(m^4n^2)$. Ill. 9, bibl. 24.