A PTAS for the Geometric Connected Facility Location Problem
We consider the Geometric Connected Facility Location Problem (GCFLP): given a set of clients C ⊂ ℝ d , one wants to select a set of locations F ⊂ ℝ d where to open facilities, each at a fixed cost f ≥0. For each client j ∈ C , one has to choose to either connect it to an open facility ϕ ( j )∈ F pa...
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| Published in: | Theory of computing systems Vol. 61; no. 3; pp. 871 - 892 |
|---|---|
| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer US
01-10-2017
Springer Nature B.V |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | We consider the Geometric Connected Facility Location Problem (GCFLP): given a set of clients
C
⊂
ℝ
d
, one wants to select a set of locations
F
⊂
ℝ
d
where to open facilities, each at a fixed cost
f
≥0. For each client
j
∈
C
, one has to choose to either connect it to an open facility
ϕ
(
j
)∈
F
paying the Euclidean distance between
j
and
ϕ
(
j
), or pay a given penalty cost
π
(
j
). The facilities must also be connected by a tree
T
, whose cost is
M
ℓ
(
T
), where
M
≥1 and
ℓ
(
T
) is the total Euclidean length of edges in
T
. The multiplication by
M
reflects the fact that interconnecting two facilities is typically more expensive than connecting a client to a facility. The objective is to find a solution with minimum cost. In this paper, we present a Polynomial-Time Approximation Scheme (PTAS) for the two-dimensional GCFLP. Our algorithm also leads to a PTAS for the two-dimensional Geometric Connected
k
-medians, when
f
=0, but only
k
facilities may be opened. |
|---|---|
| ISSN: | 1432-4350 1433-0490 |
| DOI: | 10.1007/s00224-017-9749-x |