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Let R denote a connected region inside a simple polygon, P. By building 1-dimensional barriers in P ∖ R, we want to separate from R part(s) of P of maximum area. In this paper we introduce two versions of this problem. In the budget fence version the region R is static, and there is an upper bound on the total length of barriers we may build. In the basic geometric firefighter version we assume that R represents a fire that is spreading over P at constant speed (varying speed can also be handled). Building a barrier takes time proportional to its length, and each barrier must be completed before the fire arrives. In this paper we are assuming that barriers are chosen from a given set B that satisfies a certain linearity condition. For example, this condition is satisfied for barrier curves in general position, if any two barriers cross at most once.

Approximation Algorithms for the Geometric Firefighter and Budget Fence Problems