Systems and methods are disclosed for configuring a communication network to satisfy a set of demands. A network management system can obtain a network graph representing the communication network, connectivity relationship that indicates valid pairs of edges for each vertex in the network graph, and a structure that lacks zero divisors. The network management system can use the network graph, connectivity relationship, and structure to determine a path length for which a valid path connecting a source vertex and a terminal vertex exists. The path length can be determined using a dynamic programming approach that associates an element of the structure with the collection of paths connecting the source vertex and the terminal vertex. The network management system can then use the network graph, connectivity relationship, and structure to determine a valid path of the path length that connects the source vertex and the terminal vertex.