Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
D.R. Karget , Lab. for Comput. Sci., MIT, Cambridge, MA, USA
M. Minkoff , Lab. for Comput. Sci., MIT, Cambridge, MA, USA
A networking problem of present-day interest is that of distributing a single data item to multiple clients while minimizing network usage. Steiner tree algorithms are a natural solution method, but only when the set of clients requesting the data is known. We study what can be done without this global knowledge, when a given vertex knows only the probability that any other client wishes to be connected, and must simply specify a fixed path to the data to be used in case it is requested. Our problem is an example of a class of network design problems with concave cost functions (which arise when the design problem exhibits economies of scale). In order to solve our problem, we introduce a new version of the facility location problem: one in which every open facility is required to have some minimum amount of demand assigned to it. We present a simple bicriterion approximation for this problem, one which is loose in both assignment cost and minimum demand, but within a constant factor of the optimum for both. This suffices for our application. We leave open the question of finding an algorithm that produces a truly feasible approximate solution.
trees (mathematics); facility location; uncertainty handling; client-server systems; network synthesis; approximation theory; minimisation; combinational switching; Steiner trees; incomplete global knowledge; network usage minimization; data item distribution; data-requesting clients; vertex; connection probability; fixed data path specification; network design problems; concave cost functions; economies of scale; facility location problem; open facilities; minimum demand; bicriterion approximation; assignment cost
D.R. Karget, M. Minkoff, "Building Steiner trees with incomplete global knowledge", FOCS, 2000, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2000, pp. 613, doi:10.1109/SFCS.2000.892329