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arXiv · 2011.15019

Burning graphs through farthest-first traversal

Jesús García Díaz·Julio César Pérez Sansalvador·Lil María Xibai Rodríguez Henríquez·José Alejandro Cornejo Acosta
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Abstract

The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability of a graph to contagion. This paper introduces a simple farthest-first traversal-based approximation algorithm for this problem over general graphs. We refer to this proposal as the Burning Farthest-First (BFF) algorithm. BFF runs in $O(n^3)$ steps and has an approximation factor of $3-2/b(G)$, where $b(G)$ is the size of an optimal solution. Despite its simplicity, BFF tends to generate near-optimal solutions when tested over some benchmark datasets; in fact, it returns similar solutions to those returned by much more elaborated heuristics from the literature.

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Jesús García Díaz, Julio César Pérez Sansalvador, Lil María Xibai Rodríguez Henríquez, José Alejandro Cornejo Acosta. 2020-11-30. Burning graphs through farthest-first traversal. https://doi.org/10.1109/access.2022.3159695

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