Exploring Simple Grid Polygons

  • Christian Icking
  • Tom Kamphans
  • Rolf Klein
  • Elmar Langetepe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3595)

Abstract

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.

Keywords

Robot navigation exploration covering online algorithms competitive analysis lower bounds grid polygons 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Christian Icking
    • 1
  • Tom Kamphans
    • 2
  • Rolf Klein
    • 2
  • Elmar Langetepe
    • 2
  1. 1.Praktische Informatik VIUniversity of HagenHagenGermany
  2. 2.Computer Science IUniversity of BonnBonnGermany

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