 
Summary: An Approximation Scheme for the Uncapacitated Facility
Location Problem on Planar Graphs
A. A. Ageev
Sobolev Institute of Mathematics, pr. Koptyuga 4, 630090, Novosibirsk, Russia
Abstract. We present an approximation scheme for the planar graph case of the Uncapacitated Facility
Location Problem. The scheme is based on an adaptation of the general approach due to Baker and
becomes a polynomialtime approximation scheme (PTAS) when all ratios of the transportation cost
along an edge to the cost of opening a facility at an endpoint of this edge are bounded from below by a
xed positive constant.
Keywords: facility location, polynomialtime algorithm, approximation scheme, planar graph.
Introduction
We consider a special, network case of the uncapacitated facility location problem (the
network UFLP). In a formal setting an instance of the network UFLP consists of an
undirected connected graph G = (V; E), nonnegative vertex costs c(v), nonnegative ver
tex demands '(v), and nonnegative edge lengths l(e). It is required to nd a nonempty
subset X V minimizing
F (X) =
X
v2X
c(v) +
