Approximating the probabilistic p-Center problem under pressure

The Probabilistic p -Center problem under Pressure (Min P p CP) is a variant of the usual Min p -Center problem we recently introduced in the context of wildfire management. The problem is to locate p shelters minimizing the maximum distance people will have to cover in case of fire in order to reac...

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Published in:Journal of combinatorial optimization Vol. 48; no. 1; p. 9
Main Authors: Demange, Marc, Haddad, Marcel A., Murat, Cécile
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2024
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Apexes
Approximation
Combinatorics
Computer Science
Convex and Discrete Geometry
Evacuation routing
Graph theory
Graphs
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Outbreaks
Theory of Computation
Shelter location under indeterminacy
Under pressure decision model
Variants of the
Approximation algorithms
Center problem
Probabilistic combinatorial optimization
Variants of the p-Center problem
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:The Probabilistic p -Center problem under Pressure (Min P p CP) is a variant of the usual Min p -Center problem we recently introduced in the context of wildfire management. The problem is to locate p shelters minimizing the maximum distance people will have to cover in case of fire in order to reach the closest accessible shelter. The landscape is divided into zones and is modeled as an edge-weighted graph with vertices corresponding to zones and edges corresponding to direct connections between two adjacent zones. The risk associated with fire outbreaks is modeled using a finite set of fire scenarios. Each scenario corresponds to a fire outbreak on a single zone (i.e., on a vertex) with the main consequence of modifying evacuation paths in two ways. First, an evacuation path cannot pass through the vertex on fire. Second, the fact that someone close to the fire may not take rational decisions when selecting a direction to escape is modeled using new kinds of evacuation paths. In this paper, we characterize the set of feasible solutions of Min P p CP-instance. Then, we propose some approximation results for Min P p CP. These results require approximation results for two variants of the (deterministic) Min p -Center problem called Min MAC p -Center and Min Partial p -Center.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-024-01194-y