Combinatorics: Arye Deutsch (HUJI)

Mon, 22/11/202115:00-17:00
B400 CS building

Title: The firefighter problem on 2.5 dimensions.

Consider a model of fire spreading through a graph; initially some vertices are burning, and at every given time-step fire spreads from burning vertices to their neighbors. The firefighter problem is a solitaire game in which a player is allowed, at every time-step, to protect some non-burning vertices (by effectively deleting them) in order to contain the fire growth. How many vertices per turn, on average, must be protected in order to stop the fire from spreading infinitely? Here we consider the problem on Z^2×[h] for strong adjacency. We determine the critical protection rates for this graph to be 3h. This establishes the fact that using an optimal two-dimensional strategy for all layers in parallel is asymptotically optimal.  

In the talk we will discuss the context of the problem, and see how methods from potential theory are used to tackle it. No prior knowledge on the subject will be assumed.