The Moving Firefighter Problem

The original formulation of the firefighter problem defines a discrete-time process where fire starts at designated subset vertices graph G. At each subsequent discrete time unit, propagates from burnt vertex to all its neighbors unless they are defended by that can move between any pair in single unit. Once is or defended, it remains state, and terminates when no longer spread. In this work, we present moving problem, which generalization takes u defend v determined function τ. This new models situations such as wildfire flood, firefighters have physically their current position location an entity intend defend. It also incorporates notion entities modeled not necessarily instantaneously upon arrival firefighter. We mixed-integer quadratically constrained program (MIQCP) for optimization version minimizes number case general finite graphs, arbitrary set F⊂V breaks out, firefighter, metric functions