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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| Vydáno v: | Journal of global optimization Ročník 84; číslo 3; s. 715 - 738 |
|---|---|
| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.11.2022
Springer Nature B.V |
| Témata: | |
| ISSN: | 0925-5001, 1573-2916 |
| On-line přístup: | Získat plný text |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. The max+sum spanning tree (MSST) problem is to determine a spanning tree T whose combined weight maxe∈Tw(e)+∑e∈Tc(e) is minimum for a given edge-weighted undirected network G(V, E, c, w). This problem can be solved within O(mlogn) 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 T0 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 maxe∈Eq(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(m2logn) 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. |
| Author | Jia, Junhua Guan, Xiucui Pardalos, Panos M. Zhang, Qiao Qian, Xinqiang |
| Author_xml | – sequence: 1 givenname: Junhua surname: Jia fullname: Jia, Junhua organization: School of Mathematics, Southeast University – sequence: 2 givenname: Xiucui orcidid: 0000-0002-2653-1868 surname: Guan fullname: Guan, Xiucui email: xcguan@163.com organization: School of Mathematics, Southeast University – sequence: 3 givenname: Qiao surname: Zhang fullname: Zhang, Qiao organization: School of Mathematics, Southeast University – sequence: 4 givenname: Xinqiang surname: Qian fullname: Qian, Xinqiang organization: School of Mathematics, Southeast University – sequence: 5 givenname: Panos M. surname: Pardalos fullname: Pardalos, Panos M. organization: Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, LATNA, Higher School of Economics |
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| CitedBy_id | crossref_primary_10_1007_s10898_022_01212_5 crossref_primary_10_3390_axioms14090691 crossref_primary_10_1016_j_cam_2024_116110 |
| Cites_doi | 10.1007/s10898-017-0546-5 10.1023/B:JOCO.0000038914.26975.9b 10.1016/j.tcs.2016.06.002 10.1007/s10878-020-00656-3 10.1007/s10878-006-9016-6 10.1006/jagm.1999.1052 10.1023/A:1013807829021 10.1016/j.cor.2005.12.003 10.1007/s10898-017-0554-5 10.1007/s10898-019-00852-4 10.1007/s10898-014-0140-z 10.1007/s10878-005-5486-1 10.1007/s10878-019-00433-x 10.1007/BF01589111 10.1016/0305-0548(94)90084-1 10.1007/s10898-008-9294-x 10.1287/opre.47.2.291 10.1016/j.ejor.2004.07.059 10.1007/s10898-005-6470-0 10.1016/0377-2217(94)00252-5 10.1007/s10898-011-9742-x 10.1287/opre.51.5.785.16756 10.1016/j.ejor.2007.04.031 |
| ContentType | Journal Article |
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| Keywords | Weighted Strongly polynomial time algorithm Binary search method Inverse max+sum spanning tree norm |
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| Snippet | 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... The max+sum spanning tree (MSST) problem is to determine a spanning tree T whose combined weight maxe∈Tw(e)+∑e∈Tc(e) is minimum for a given edge-weighted... |
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| SubjectTerms | Algorithms Computer Science Graph theory Iterative methods Linear programming Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Polynomials Real Functions |
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| Title | Inverse max+sum spanning tree problem under weighted l∞ norm by modifying max-weight vector |
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