Patent US 9,596,125

The Location Design and Routing problem asks to find a subset of “depot” nodes and a spanning forest of a graph such that every connected component in the forest contains at least one depot. This problem arises in a number of both logistical and computer networking problems, for example, in selecting the number and location of distribution centers in vehicle routing networks. This problem is functionally equivalent to that of supernode selection in peer-to-peer networks. A distributed algorithm approximates a solution to this problem that runs in a logarithmic number of communication rounds with respect to the number of nodes (independent of the topology of the network), and, under assumptions on the embedding of the edge weights, whose solutions are within a factor of 2 of optimal.