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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Exploring Simple Grid Polygons
verfasst von : Christian Icking, Tom Kamphans, Rolf Klein, Elmar Langetepe
Erschienen in: Computing and Combinatorics
Verlag: Springer Berlin Heidelberg
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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.