Cost Function Firefighter Simulation Data

# ReadmeThis repo contains the results of simulations of a variant of the Firefighter problem performed on a range of real-world and randomly generated graphs. Specifically, the variant is called the Cost Function Firefighter problem[^1]. These data are in a publication currently under review.## Cost Function FirefighterThe Firefighter problem is a discrete-time decision problem that, given a rooted graph $(G, r)$ and a target integer $k$, asks whether at least $k$ vertices can be saved in $G$ by defending one per turn if the fire starts at $r$. In our cost function variant, we assign a cost to defend to each vertex via various methods. We are given an integer budget $b$ that the sum of the costs of the vertices selected for defence in that turn must not exceed. For our simulations, cost functions are assigned by one of the following functions: Uniform (all costs are 1)Uniformly random (costs chosen uniformly at random from default range $[1,5]$ unless otherwise specified)Binary hesitation (2 with given probability, defaults to 29.72%, 1 otherwise)Threat with stochasticity (costs are inversely proportional to proximity to fire - closer fire means higher threat, so lower cost - with added stochastic noise of a specified level)In simulations, we run several heuristics on each graph with each of these cost functions. These heuristics are greedy on:Highest degreeLowest costHighest threat (closest vertex to fire)And ties can be broken for one heuristic by either of the other two. We also run a random defence strategy for comparison.For the data contained in this repository, we ran 50 trials for each of the combinations of . The graphs used are: two real-world plots, also included in the repo (`network-data-in`): contact networks of raccoons and sleepy lizards, and eight random graphs. We used Networkx for generation:Barabási-Albert graphs, input edges 1, 2, 3, 5, 8, 10Erdős–Rényi graphs, generation probabilities 0.05, 0.10, 0.15, 0.20, 0.25Watts-Strogatz, mean degrees 4, 6, 8, 10Clustered power-law graphs, on input edges 2, 3, 4 and 5 per vertexScale-freeRandom geometric with radii 0.05, 0.10, 0.15, 0.20 and 0.25Random $r$-regular for $r=2, 3, 4, 6, 8$\Connected caveman with 5, 10, 15 and 20 cliques (as close as possible to 100 vertices)References:[^1]: E Hunter and J Enright, The Firefighter Game with State-varying Cost Functions, _Proceedings of The Thirteenth International Conference on Complex Networks and their Applications: COMPLEX NETWORKS 2024,_ 2025, Ed. H Cherifi, M Donduran, L M Rocha, C Cherifi and O Varol, vol. 4, no. 1