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.<br>## Cost Function Firefighter<br>The 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. <br>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.<br>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)<br>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