Authors:
Marc Demange
and
Cerasela Tanasescu
Affiliation:
RMIT University, Australia
Keyword(s):
Multi-period Vertex Cover, Wildfire, Fuel Management, Planar Graphs, Polynomial Approximation, Approximation Preserving Reductions.
Related
Ontology
Subjects/Areas/Topics:
Applications
;
Artificial Intelligence
;
Energy and Environment
;
Knowledge Discovery and Information Retrieval
;
Knowledge-Based Systems
;
Mathematical Modeling
;
Methodologies and Technologies
;
Operational Research
;
Optimization
;
Pattern Recognition
;
Software Engineering
;
Symbolic Systems
Abstract:
We consider a generalisation of MIN WEIGHTED VERTEX COVER motivated by a problem in wildfire prevention. The problem is defined for a fixed number of time periods and we have to choose, at each period, some vertices to be deleted such that we never have two adjacent remaining vertices. The specificity is that whenever a vertex is deleted it reappears after a given number of periods. Consequently we may need to delete a single vertex several times. The objective is to minimise the total weight (cost) of deleted vertices. The considered application motivates the case of planar graphs. While similar problems have been mainly solved using mixed integer linear models (MIP) we investigate a graph approach that allows to take into account the structure of the underlying graph. We use a reduction to the usual MIN WEIGHTED VERTEX COVER to devise efficient approximation algorithms and to raise some polynomial classes.