Minimizing the expense transmission time from the source node to demand nodes
An undirected graph G = ( V , A ) by a set V of n nodes, a set A of m edges, and two sets S , D ⊆ V consists of source and demand nodes are given. This paper presents two new versions of location problems which are called the f ( σ ) -location and g ( σ ) -location problems. We define an f ( σ ) -lo...
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| Veröffentlicht in: | Journal of combinatorial optimization Jg. 47; H. 3; S. 47 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
01.04.2024
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 1382-6905, 1573-2886 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | An undirected graph
G
=
(
V
,
A
)
by a set
V
of
n
nodes, a set
A
of
m
edges, and two sets
S
,
D
⊆
V
consists of source and demand nodes are given. This paper presents two new versions of location problems which are called the
f
(
σ
)
-location and
g
(
σ
)
-location problems. We define an
f
(
σ
)
-location of the network
N
as a node
s
∈
S
with the property that the maximum expense transmission time from the node
s
to the destinations of
D
is as cheap as possible. The
f
(
σ
)
-location problem divides the range
(
0
,
∞
)
into intervals
∪
i
(
a
i
,
b
i
)
and finds a source
s
i
∈
S
, for each interval
(
a
i
,
b
i
)
, such that
s
i
is a
f
(
σ
)
-location for each
σ
∈
(
a
i
,
b
i
)
. Also, define a
g
(
σ
)
-location as a node
s
of
S
with the property that the sum of expense transmission times from the node
s
to all destinations of
D
is as cheap as possible. The
g
(
σ
)
-location problem divides the range
(
0
,
∞
)
into intervals
∪
i
(
a
i
,
b
i
)
and finds a source
s
i
∈
S
, for each interval
(
a
i
,
b
i
)
, such that
s
i
is a
g
(
σ
)
-location for each
σ
∈
(
a
i
,
b
i
)
. This paper presents two strongly polynomial time algorithms to solve
f
(
σ
)
-location and
g
(
σ
)
-location problems. |
|---|---|
| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1382-6905 1573-2886 |
| DOI: | 10.1007/s10878-024-01113-1 |