2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2000)

Redondo Beach, California

Nov. 12, 2000 to Nov. 14, 2000

ISSN: 0272-5428

ISBN: 0-7695-0850-2

pp: 613

M. Minkoff , Lab. for Comput. Sci., MIT, Cambridge, MA, USA

D.R. Karget , Lab. for Comput. Sci., MIT, Cambridge, MA, USA

ABSTRACT

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.

INDEX TERMS

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

CITATION

M. Minkoff,
D.R. Karget,
"Building Steiner trees with incomplete global knowledge",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 613, 2000, doi:10.1109/SFCS.2000.892329