Burning Graphs Through Farthest-First Traversal

Dı́az, Jesús; Sansalvador, Julio César Pérez; Henriquez, Lil Maria Rodriguez; Acosta, Jose

doi:10.1109/access.2022.3159695

Cited by 9 publications

(11 citation statements)

References 25 publications

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“…Second, to understand the differences in the interfilament contacts among the clusters, we performed graph burning studies ( Bonato et al. , 2016 ; Garcia-Diaz et al. , 2022 ).…”

Section: Resultsmentioning

confidence: 99%

Computational simulations reveal that Abl activity controls cohesiveness of actin networks in growth cones

Chandrasekaran

Clarke

McQueen

et al. 2022

MBoC

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“…Second, to understand the differences in the interfilament contacts among the clusters, we performed graph burning studies ( Bonato et al. , 2016 ; Garcia-Diaz et al. , 2022 ).…”

Section: Resultsmentioning

confidence: 99%

Computational simulations reveal that Abl activity controls cohesiveness of actin networks in growth cones

Chandrasekaran

Clarke

McQueen

et al. 2022

MBoC

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“…These results have been improved very recently. García-Díaz et al [10] have given a (3 − 2/b)-approximation algorithm where b is the burning number of the input graph. Mondal et al [17] have shown the graph burning problem to be APX-hard, even in a generalized setting where k = O(1) vertices can be chosen to initiate the fire at each step.…”

Section: Related Resultsmentioning

confidence: 99%

Burning Number for the Points in the Plane

Keil¹,

Mondal²,

Moradi³

2022

Preprint

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The burning process on a graph G starts with a single burnt vertex, and at each subsequent step, burns the neighbors of the currently burnt vertices, as well as one other unburnt vertex. The burning number of G is the smallest number of steps required to burn all the vertices of the graph. In this paper, we examine the problem of computing the burning number in a geometric setting. The input is a set of points P in the Euclidean plane. The burning process starts with a single burnt point, and at each subsequent step, burns all the points that are within a distance of one unit from the currently burnt points and one other unburnt point. The burning number of P is the smallest number of steps required to burn all the points of P . We call this variant point burning. We consider another variant called anywhere burning, where we are allowed to burn any point of the plane. We show that point burning and anywhere burning problems are both NP-complete, but (2 + ε) approximable for every ε > 0. Moreover, if we put a restriction on the number of burning sources that can be used, then the anywhere burning problem becomes NP-hard to approximate within a factor of 2 √ 3 − ε.

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“…The optimization version of the problem also remains NP-hard for trees and graphs with disjoint paths [7]. Regarding arbitrary graphs, two approximation algorithms are reported in the literature; they have an approximation factor of 3 and 3 − 2/b(G), respectively [7,8]. There is a 2-approximation algorithm for trees, a 1.5-approximation algorithm for graphs with disjoint paths, and a 2-approximation algorithm for square grids [6,7].…”

Section: Definitionmentioning

confidence: 99%

“…Some of these proposals are based on centrality measures and binary search over the possible values of the burning number b(G). According to experimental results, these heuristics and approximation algorithms have an acceptable performance [4][5][6][7][8]. However, they do not guarantee to find optimal solutions.…”

Section: Introductionmentioning

confidence: 99%

Graph Burning: Mathematical Formulations and Optimal Solutions

et al. 2022

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The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify how vulnerable a graph is to contagion. This paper introduces three mathematical formulations of the problem: an integer linear program (ILP) and two constraint satisfaction problems (CSP1 and CSP2). Thanks to off-the-shelf optimization software, these formulations can be solved optimally over arbitrary graphs; this is relevant because the only algorithms designed to date for this problem are approximation algorithms and heuristics, which do not guarantee to find optimal solutions. We empirically compared the proposed formulations using random graphs and off-the-shelf optimization software. The results show that CSP1 and CSP2 tend to reach optimal solutions in less time than the ILP. Therefore, we executed them over some benchmark graphs of order at most 5908. The previously best-known solutions for some of these graphs were improved. We draw some empirical observations from the experimental results. For instance, we find the tendency: the larger the graph’s optimal solution, the more difficult it is to find it. Finally, the resulting set of optimal solutions might be helpful as a benchmark dataset for the performance evaluation of non-exact algorithms.

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Burning Graphs Through Farthest-First Traversal

Cited by 9 publications

References 25 publications

Computational simulations reveal that Abl activity controls cohesiveness of actin networks in growth cones

Computational simulations reveal that Abl activity controls cohesiveness of actin networks in growth cones

Burning Number for the Points in the Plane

Graph Burning: Mathematical Formulations and Optimal Solutions

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