Inverse max+sum spanning tree problem under weighted l∞ norm by modifying max-weight vector
The max+sum spanning tree ( MSST ) problem is to determine a spanning tree T whose combined weight max e ∈ T w ( e ) + ∑ e ∈ T c ( e ) is minimum for a given edge-weighted undirected network G ( V , E , c , w ). This problem can be solved within O ( m log n ) time, where m and n are the numbers o...
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| Published in: | Journal of global optimization Vol. 84; no. 3; pp. 715 - 738 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer US
01.11.2022
Springer Nature B.V |
| Subjects: | |
| ISSN: | 0925-5001, 1573-2916 |
| Online Access: | Get full text |
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| Summary: | The max+sum spanning tree (
MSST
) problem is to determine a spanning tree
T
whose combined weight
max
e
∈
T
w
(
e
)
+
∑
e
∈
T
c
(
e
)
is minimum for a given edge-weighted undirected network
G
(
V
,
E
,
c
,
w
). This problem can be solved within
O
(
m
log
n
)
time, where
m
and
n
are the numbers of edges and nodes, respectively. An inverse
MSST
problem (
IMSST
) aims to determine a new weight vector
w
¯
so that a given
T
0
becomes an optimal
MSST
of the new network
G
(
V
,
E
,
c
,
w
¯
)
. The
IMSST
problem under weighted
l
∞
norm is to minimize the modification cost
max
e
∈
E
q
(
e
)
|
w
¯
(
e
)
-
w
(
e
)
|
, where
q
(
e
) is a cost modifying the weight
w
(
e
). We first provide some optimality conditions of the problem. Then we propose a strongly polynomial time algorithm in
O
(
m
2
log
n
)
time based on a binary search and a greedy method. There are
O
(
m
) iterations and we solve an
MSST
problem under a new weight in each iteration. Finally, we perform some numerical experiments to show the efficiency of the algorithm. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0925-5001 1573-2916 |
| DOI: | 10.1007/s10898-022-01170-y |