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Published in:
2007 | OriginalPaper | Chapter
Network Design with Edge-Connectivity and Degree Constraints
Authors : Takuro Fukunaga, Hiroshi Nagamochi
Published in: Approximation and Online Algorithms
Publisher: Springer Berlin Heidelberg
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We consider the following network design problem; Given a vertex set
V
with a metric cost
c
on
V
, an integer
k
≥1, and a degree specification
b
, find a minimum cost
k
-edge-connected multigraph on
V
under the constraint that the degree of each vertex
v
∈
V
is equal to
b
(
v
). This problem generalizes metric TSP. In this paper, we propose that the problem admits a
ρ
-approximation algorithm if
b
(
v
)≥2,
v
∈
V
, where
ρ
=2.5 if
k
is even, and
ρ
=2.5+1.5/
k
if
k
is odd. We also prove that the digraph version of this problem admits a 2.5-approximation algorithm and discuss some generalization of metric TSP.