Table 1.
Comparison of tractability and hardness results for Fire and Cost-Fire for graphs on n vertices and m edges, maximum path length and budget b. Pathcontainable is defined in Sect 4.4.
Fig 1.
Illustration of a strategy for an instance of Cost-Fire on the depicted graph on 9 vertices, rooted at r, where each vertex costs 1 to defend and a budget of 2 per turn is available.
Fig 2.
Construction of a (2n, n + 2m)-Sea Fan graph used in the reduction in the proof of Theorem 4; vertex labels correspond to variables and clauses in the 2N2P-SAT instance.
Fig 3.
Illustration of the strategy used in the proof of Theorem 5 (to show that Fire on an (f, )-Sea Fan graph is tractable).
Open vertices are unfilled, burning are filled in red and defended are filled black.
Fig 4.
Visualisation and degree rank plot of a social interaction graph of sleepy lizards due to Bull et al. [24].
In the graph visualisation, larger vertices indicate higher degrees.
Fig 5.
Visualisation and degree rank plot of the raccoon contact graph constructed by Reynolds et al. [27] used to simulate heuristics.
Larger vertices indicate higher degrees.
Fig 6.
Plots of median numbers of vertices saved by various heuristics on an interaction graph of 60 sleepy lizards.
Fig 7.
Plots of median numbers of vertices saved on an interaction graph of 24 raccoons by various heuristics.
Fig 8.
Plots of median numbers of vertices saved on randomly generated Erdős-Rényi graphs on 100 vertices with generation probability 0.05.
Fig 9.
Plots of median numbers of vertices saved on randomly generated Erdős-Rényi graphs on 100 vertices with generation probability 0.20.
Fig 10.
Plots of median numbers of vertices saved on randomly generated Barabási-Albert graphs on 100 vertices with 2 edges added per vertex.
Fig 11.
Plots of median numbers of vertices saved on randomly generated Barabási-Albert graphs on 100 vertices with 10 edges added per vertex.
Fig 12.
Plots of median numbers of vertices saved on randomly generated clustered power-law graphs on 100 vertices with 2 edges added per vertex.
Fig 13.
Plots of median numbers of vertices saved on randomly generated clustered power-law graphs on 100 vertices with 5 edges added per vertex.
Fig 14.
Plots of median numbers of vertices saved on Watts-Strogatz graphs on 100 vertices with mean degree 4.
Fig 15.
Plots of median numbers of vertices saved on Watts-Strogatz graphs on 100 vertices with mean degree 10.
Fig 16.
Plots of median numbers of vertices saved on caveman graphs on 100 vertices arranged in 10 cliques of size 10.
Fig 17.
Plots of median numbers of vertices saved on caveman graphs on 100 vertices arranged in 20 cliques of size 5.
Fig 18.
Median numbers of vertices saved on randomly generated geometric graphs on 100 vertices with radius 0.15.
Fig 19.
Median numbers of vertices saved on randomly generated geometric graphs on 100 vertices with radius 0.25.
Fig 20.
Plots of median numbers of vertices saved on randomly generated 3-regular graphs on 100 vertices.
Fig 21.
Plots of median numbers of vertices saved on randomly generated 8-regular graphs on 100 vertices.