S. Koenig. Open Problem: Analyzing Ant Robot Coverage. In International Conference on Learning Theory (COLT), pages 312-313, 2010.

Abstract: Ant robots can repeatedly and robustly cover terrain by always moving away from the trails that they leave in the terrain. This coverage strategy can be modeled with graph traversal strategies similar to real-time search methods (such as Learning Real-Time A*) and reinforcement learning methods (such as Real-Time Dynamic Programming). The resulting worst-case cover times are known to be exponential in the number of vertices on both directed and undirected graphs in general. The known undirected graphs with large worst-case cover times have unbounded degree vertices. However, existing ant robots navigate on grids, a special case of undirected planar graphs with bounded degree vertices. Their experimental cover times appear to scale almost identically to those of coverage strategies with polynomial worst-case cover times. However, it is an open problem to prove whether the resulting worst-case cover times on grids are indeed polynomial in the number of vertices.

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