Affiliation:
1. Microsoft Research, Redmond, WA
2. The Chinese University of Hong Kong, Shatin, Hong Kong
Abstract
In the
Minimum Bounded Degree Spanning Tree
problem, we are given an undirected graph
G
= (
V, E
) with a degree upper bound
B
v
on each vertex
v
∈
V
, and the task is to find a spanning tree of minimum cost that satisfies all the degree bounds. Let
OPT
be the cost of an optimal solution to this problem. In this article we present a polynomial-time algorithm which returns a spanning tree
T
of cost at most
OPT
and
d
T
(
v
) ≤
B
v
+ 1 for all
v
, where
d
T
(
v
) denotes the degree of
v
in
T
. This generalizes a result of Fürer and Raghavachari [1994] to weighted graphs, and settles a conjecture of Goemans [2006] affirmatively. The algorithm generalizes when each vertex
v
has a degree lower bound
A
v
and a degree upper bound
B
v
, and returns a spanning tree with cost at most
OPT
and
A
v
- 1 ≤
d
T
(
v
) ≤
B
v
+ 1 for all
v
∈
V
. This is essentially the best possible. The main technique used is an extension of the iterative rounding method introduced by Jain [2001] for the design of approximation algorithms.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
35 articles.
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