Proceedings 41st Annual Symposium on Foundations of Computer Science (2000)
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
M. Minkoff and D. Karget, "Building Steiner trees with incomplete global knowledge," Proceedings 41st Annual Symposium on Foundations of Computer Science(FOCS), Redondo Beach, California, 2000, pp. 613.