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An exact algorithm for disaster-resilience augmentation of planar straight-line graphs

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  • Alexander Westcott

    (University of Melbourne)

  • Charl Ras

    (University of Melbourne)

Abstract

We consider the problem of adding a minimum length set of edges to a geometric graph so that the resultant graph is resilient against partition from the effect of a single disaster. Disasters are modeled by discs of given maximum radius, and a disaster destroys all edges intersecting its interior. It is assumed that the input and output graphs are planar with a straight-line embedding. We provide a computationally simple characterisation of feasible input instances in terms of the convex hull of the given graph, and present a fast ILP algorithm for generating optimal solutions. We also perform a computational study which shows that our algorithm is able to solve randomly generated instances with hundreds of nodes.

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  • Alexander Westcott & Charl Ras, 2025. "An exact algorithm for disaster-resilience augmentation of planar straight-line graphs," Journal of Global Optimization, Springer, vol. 92(2), pages 483-508, June.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:2:d:10.1007_s10898-024-01459-0
    DOI: 10.1007/s10898-024-01459-0
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