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Open problems: 16

Open problems: 16 Open Problems: 16 Samir Khuller Department of Computer Science University of Maryland, College Park, MD 20742 samir@cs, umd. edu Copyright @ Samir Khuller, 1997 For this column, I include two problems that came to my attention recently, together with a list of problems posted by David Williamson (IBM Research) at the Dagstuhl workshop on Approximation Algorithms in August 1997. I have added references and remarks to his list of problems (which has been shortened slightly). All contributors: please provide short descriptions of the problems, with references. Problems: 1. M i n C o s t N e t w o r k C o n s t r u c t i o n Given a graph G = (V, E) with pairs of vertices (s~, ~i) that have demand di. For each edge e, we have an installation cost of w(e) (weight of the edge) and capacity C. Find a minimum weight set of edges to install, so that we can route the entire demand di for each demand pair. The problem is NP-hard. Is there a constant factor approximation? Using Bartal's result [2] on approximating metric spaces by tree metrics, Awerbuch and Azar [1] have shown http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGACT News Association for Computing Machinery

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