A Multi-Commodity Flow Approach for the Design of the Last Mile in Real-World Fiber Optic Networks

We consider the problem of finding a most cost-efficient fiber optic network to connect given customer nodes to an existing network infrastructure. Given is a connected undirected graph G = (V, E, c, l, p, kmax) describing the topology of the surrounding area of given customer nodes. Each edge e = (i, j) ∈ E represents a straight segment of Euclidean length le ≥ 0 where a fiber optics cable might be installed with construction costs ce ≥ 0. The existing infrastructure is given as a subgraph I = (VI , EI) of G. Furthermore the set of nodes V consists of the customer nodes C that shall be connected and spatial nodes S (possible Steiner nodes) resulting from the underlying spatial topology. The customer set C is the disjoint union of C1 and C2, whereby customers C1 require a single connection and customers C2 need to be redundantly connected.