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We study a greedy mapping method that always moves the robot from its current location to the closest location that it has not visited (or observed) yet, until the terrain is mapped. Although one does not expect such a simple mapping method to minimize the travel distance of the robot, we present analytical results that show (perhaps surprisingly) that the travel distance of the robot is reasonably small. This is interesting because greedy mapping has a number of desirable properties. It is simple to implement and integrate into complete robot architectures. It does not need to have control of the rebut at all times, takes advantage of prior knowledge about parts of the terrain (if available), and can be used by several robots cooperatively.