Abstract
We consider the problem of a robot inside an unknown polygon that has to find a path from a starting point s to a target point t. We assume that it is equipped with an on-board vision system through which it can get the visibility map of its surroundings. Furthermore, we assume that the robot is contained in a simple polygon that belongs to the class of polygons called generalized streets. We consider three problems.
-
1.
We present a strategy that allows the robot to search for t in an arbitrarily oriented generalized street where the distance travelled by the robot under our strategy is at most 80 times the length of the shortest path from s to t.
-
2.
We show that there are orthogonal generalized streets for which the distance travelled by the robot under any searching strategy is at least 9.06 times the length of the shortest path from s to t.
-
3.
Finally, we show that even if the location of the target is known, there are orthogonal generalized streets for which the distance travelled by the robot under any searching strategy is at least 9 times the length of the shortest path from s to t.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This research is supported by the DFG-Project ”Diskrete Probleme”, No. Ot 64/8-1. Part of this research was done while the first author was at the Department of Computer Science, University of Waterloo
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
R. Baeza-Yates, J. Culberson and G. Rawlins. “Searching in the plane”, Information and Computation, Vol. 106, (1993), pp. 234–252.
A. Blum, P. Raghavan and B. Schieber. “Navigating in unfamiliar geometric terrain“, Proc. of 23rd ACM Symp. on Theory of Computing, (1991), pp. 494–504.
K-F. Chan and T. W. Lam. “An on-line algorithm for navigating in an unknown environment”, International Journal of Computational Geometry & Applications, Vol. 3, (1993), pp. 227–244.
A. Datta, Ch. Hipke, and S. Schuierer. “Competitive searching in polygons—beyond generalized streets”, Proc. Sixth Annual International Symposium on Algorithms and Computation, (1995), pp. 32–41. LNCS 1004.
A. Datta and Ch. Icking. “Competitive searching in a generalized street”, Proc. 10th ACM Symp. on Computational Geometry, (1994), pp. 175–182.
X. Deng, T. Kameda and C. Papadimitriou. “How to learn an unknown environment I: The rectilinear case”, Technical Report CS-93-04, Dept. of Comp. Sci., York University, 1993. Also as Proc. 32nd IEEE Symp. on Foundations of Comp. Sci., (1991), pp. 298–303.
Ch. Icking. Ph. D. Thesis, Fernuniversität Hagen, 1994.
B. Kalyasundaram and K. Pruhs. “A competitive analysis of algorithms for searching unknown scenes”, Computational Geometry: Theory and Applications 3, (1993), pp. 139–155.
R. Klein. “Walking an unknown street with bounded detour”, Computational Geometry: Theory and Applications 1, (1992), pp. 325–351.
J. Kleinberg. “On-line search in a simple polygon”, Proc. of 5th ACM-SIAM Symp. on Discrete Algorithms, (1994), pp. 8–15.
A. Lopez-Ortiz. “On-line searching on bounded and unbounded domains”, Ph.D. thesis, University of Waterloo, Waterloo, Canada, 1996.
A. Lopez-Ortiz and S. Schuierer. “Going home through an unknown street”, Proc. of 4th Work-shop on Data Structures and Algorithms, 1995, LNCS 955, pp. 135–146.
A. Lopez-Ortiz and S. Schuierer. “Simple, Efficient and Robust Strategies to Traverse Streets”, Proc. 7th Canad. Conf. on Computational Geometry, 1995, pp. 217–222.
A. Mei and Y. Igarashi. “Efficient strategies for robot navigation in unknown environment” Proc. of 21st Intl. Colloquium on Automata, Languages and Programming, (1994).
E. Moise. “Elementary Geometry from an Advanced Standpoint”, 2nd ed., Addison-Wesley, 1973.
C. H. Papadimitriou and M. Yannakakis. “Shortest paths without a map”, Theoretical Computer Science 84, (1991), pp. 127–150.
D. D. Sleator and R. E. Tarjan. “Amortized efficiency of list update and paging rules”, Communications of the ACM 28, (1985), pp. 202–208.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
López-Ortiz, A., Schuierer, S. (1996). Generalized streets revisited. In: Diaz, J., Serna, M. (eds) Algorithms — ESA '96. ESA 1996. Lecture Notes in Computer Science, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61680-2_81
Download citation
DOI: https://doi.org/10.1007/3-540-61680-2_81
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61680-1
Online ISBN: 978-3-540-70667-0
eBook Packages: Springer Book Archive