Computational Geometry Column 63

Abstract

Assume that a fire spreads inside a geometric environment. The fire-fighter's task is to extinguish the fire, or to build a barrier that encloses and stops the fire. This problem has been considered in many different models and variants. For example, the spreading can occur in a discrete world or in the continuous plane. Many computational questions arise. How fast must the fighters be in comparison to the fire's speed, in order to fulfill their task? How many fire-fighters are necessary and sufficient? How can they enclose the fire as efficiently as possible? Of the wealth of existing results we present some appetizers indicating the wide range of this topic, and mention a number of open questions.