Budget Constrained Minimum Cost Connected Medians

Abstract

Several practical instances of network design problems require the network to satisfy multiple constraints. In this paper, we address the Budget Constrained Connected Median Problem: We are given an undirected graph G = (V,E) with two different edge-weight functions c (modeling the construction or communication cost) and d (modeling the service distance), and a bound B on the total service distance. The goal is to find a subtree T of G with minimum c-cost c(T) subject to the constraint that the sum of the service distances of all the remaining nodes v ∈ V T to their closest neighbor in T does not exceed the speci- fied budget B. This problem has applications in optical network design and the efficient maintenance of distributed databases.

We formulate this problem as bicriteria network design problem, and present bicriteria approximation algorithms. We also prove lower bounds on the approximability of the problem that demonstrate that our performance ratios are close to best possible.

Supported by an NSF CAREER grant CCR-9625297 and DOE Contract W-7405- ENG-36

Research supported by the German Science Foundation (DFG, grant Gr 883/5-3).

Research supported by the Department of Energy under Contract W-7405-ENG-36.