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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Published in:Journal of combinatorial optimization Vol. 47; no. 3; p. 47
Main Authors: Ghiyasvand, Mehdi, Keshtkar, Iman
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2024
Springer Nature B.V
Subjects:
Algorithms
Combinatorics
Commodities
Convex and Discrete Geometry
Costs
Intervals
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nodes
Operations Research/Decision Theory
Optimization
Polynomials
Theory of Computation
Facility location problem
Quickest path
The expense transmission time
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary: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.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-024-01113-1