An Improved Strategy for Exploring a Grid Polygon

We study the problem of exploring a simple grid polygon using a mobile robot. The robot starts from a location which is adjacent to the boundary of the polygon, and after exploring all the squares, has to return to its starting location. The robot is equipped with memory, but has no prior knowledge of the explored terrain. The view of the terrain is restricted to the four squares directly adjacent to the robot’s current location. The performance of the exploration strategy is measured in terms of the competitive ratio, with respect to the length of the optimal path for an exploration with complete knowledge of the terrain. We propose a new exploration strategy which achieves a competitive ratio of 5/4, whereas the previously best approach [Icking, Kamphans, Klein, and Langetepe; Proc. COCOON’05 ] has a competitive ratio of 4/3. The analysis for our algorithm is tight. Moreover, we show that no exploration strategy is ever better than 20/17-competitive, thus improving the previous lower bound of 7/6.