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Exploring simple grid polygons. (English) Zbl 1128.68504
Wang, Lusheng (ed.), Computing and combinatorics. 11th annual international conference, COCOON 2005, Kunming, China, August 16–29, 2005. Proceedings. Berlin: Springer (ISBN 3-540-28061-8/pbk). Lecture Notes in Computer Science 3595, 524-533 (2005).
Summary: We investigate the online exploration problem of a short-sighted mobile robot moving in an unknown cellular room without obstacles. The robot has a very limited sensor; it can determine only which of the four cells adjacent to its current position are free and which are blocked, i.e., unaccessible for the robot. Therefore, the robot must enter a cell in order to explore it. The robot has to visit each cell and to return to the start. Our interest is in a short exploration tour, i.e., in keeping the number of multiple cell visits small. For abitrary environments without holes we provide a strategy producing tours of length \(S \leq C + \frac{1}{2} E - 3\), where \(C\) denotes the number of cells – the area –, and \(E\) denotes the number of boundary edges – the perimeter – of the given environment. Further, we show that our strategy is competitive with a factor of \(\frac43\), and give a lower bound of \(\frac76\) for our problem. This leaves a gap of only \(\frac16\) between the lower and the upper bound.
For the entire collection see [Zbl 1078.68006].

68T40 Artificial intelligence for robotics
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
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