Connected facility leasing problems

We study leasing variants of the connected facility location problem, in which we wish to connect a set of clients to facilities, and facilities are connected via core edges, whose cost is a scale factor times the cost of a simple edge. We identify two aspects of the problem that can lead to different variants: (a) if there is a single or multiple commodities, and (b) if we lease facilities and buy core edges, or if we lease both facilities and core edges. Combining these aspects, we propose four variants of the problem, and we give approximation and competitive online algorithms for each of them when the (smallest) scale factor is 1. The algorithms we propose follow the technique of combining available algorithms for the underlying facility leasing and Steiner problems.