A New Model in Firefighting Theory

TL;DR

This paper introduces a new discrete hexagonal cell graph model for firefighting problems, providing efficient algorithms for some variants and NP-completeness results for others, advancing theoretical understanding.

Contribution

It presents a novel, more general firefighting framework based on hexagonal grids, with algorithms and complexity results for multiple problem variants.

Findings

Two firefighting problems solved with polynomial algorithms

One problem proven NP-complete

Model extensions discussed with complexity implications

Abstract

Continuous and discrete models for firefighting problems are well-studied in Theoretical Computer Science. We introduce a new, discrete, and more general framework based on a hexagonal cell graph to study firefighting problems in varied terrains. We present three different firefighting problems in the context of this model; for two of which, we provide efficient polynomial time algorithms and for the third, we show NP-completeness. We also discuss possible extensions of the model and their implications on the computational complexity.