Optimization Letters (2008) 2:171–175
DOI 10.1007/s11590-007-0051-8
ORIGINAL PAPER
An approximation algorithm for network design
problems with downwards-monotone demand functions
Michael Laszlo · Sumitra Mukherjee
Received: 14 December 2006 / Accepted: 28 March 2007 / Published online: 28 April 2007
© Springer-Verlag 2007
Abstract Building on an existing 2-approximate algorithm for the class of network
design problems with downwards-monotone demand functions, many of which are
NP-hard, we present an algorithm that produces solutions that are at least as good as
and typically better than solutions produced by the existing algorithm.
Keywords Network design problems · Approximation algorithms ·
Spanning forests · Integer programs
1 Introduction
Given an undirected graph G = (V , E ) with non-negative edge costs c
e
on all edges
e ∈ E , and a demand function f : 2
V
→ N, the network design problem may be
characterized by the following integer program (IP):
Minimize
e∈E
c
e
x
e
subject to:
x (δ( S)) ≥ f ( S) φ = S ⊂ V ,
x
e
integer e ∈ E ,
where δ( S) denotes the set of edges with exactly one endpoint in S, and x ( F ) =
∑
e∈F
x
e
. See [1, 4] for discussions of this formulation of network design problems.
M. Laszlo (B ) · S. Mukherjee
Graduate School of Computer and Information Sciences,
Nova Southeastern University, Fort Lauderdale, FL 33314, USA
e-mail: mjl@nova.edu
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