Searching Rectilinear Streets Completely
We consider the on-line navigation problem of a robot inside an unknown polygon P. The robot has to find a path from a starting point to an unknown goal point and it is equipped with on-board cameras through which it can get the visibility map of its immediate surroundings. It is known that if P is a street with respect to two points s and t then starting at s the robot can find t with a constant competitive ratio. In this paper we consider the case where the robot is inside a rectilinear street but looks for an arbitrary goal point g instead of t. Furthermore, it may start at some point different from s. We show that in both cases a constant competitive ratio can be achieved and establish lower bounds for this ratio. If the robot starts at s, then our lower and upper bound match, that is, our algorithm is optimal.
KeywordsSearch Direction Competitive Ratio Simple Polygon Competitive Strategy Search Path
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- [BBF+96]P. Berman, A. Blum, A. Fiat, H. Karloff, A. Rosén, and M. Saks. Randomized robot navigation algorithms. In Proc. 7th ACM-SIAM Symp. On Discrete Algorithms, 1996.Google Scholar
- [BRS91]A. Blum, P. Raghavan, and B. Schieber. Navigating in unfamiliar geometric terrain. In Proc. 23rd ACM Sympos. Theory Comput., pages 494–503, 1991.Google Scholar
- [DHS95]A. Datta, Ch. Hipke, and S. Schuierer. Competitive searching in polygons-beyond generalized streets. In J. Staples, P. Eades, N. Katoh, and A. Moffat, editors, Proc. Sixth Annual International Symposium on Algorithms and Computation, pages 32–41. LNCS 1004, 1995.Google Scholar
- [DI94]A. Datta and Ch. Icking. Competitive searching in a generalized street. In Proc. of the 10th Annual ACM Symp. on Computational Geometry, pages 175–182, 1994.Google Scholar
- [ELW93]P. Eades, X. Lin, and N. C. Wormald. Performance guarantees for motion planning with temporal uncertainty. The Australian Computer Journal, 25(1):21–28, 1993.Google Scholar
- [Gal80]S. Gal. Search Games. Academic Press, 1980.Google Scholar
- [IKL99]Ch. Icking, R. Klein, and E. Langetepe. An optimal competitive strategy for walking in streets. In Proc. 16th Annual Symposium on Theoretical Aspects of Computer Science, pages 110–120, LNCS 1563, 1999.Google Scholar
- [Kle91]R. Klein. Walking an unknown street with bounded detour. In Proc. 32nd IEEE Symp. On Foundations of Computer Science, pages 304–313, 1991.Google Scholar
- [Kle94]J. M. Kleinberg. On-line search in a simple polygon. In Proc. 5th ACM-SIAM Symp. on Discrete Algorithms, pages 8–15, 1994.Google Scholar
- [Sch97]S. Schuierer. On-line searching in geometric trees. In Proc. 9th Canadian Conf. On Computational Geometry, pages 135–140, 1997.Google Scholar
- [SS99]S. Schuierer and I. Semrau. An optimal strategy for searching in unknown streets. In Proc. 16th Annual Symposium on Theoretical Aspects of Computer Science, pages 121–131, LNCS 1563, 1999.Google Scholar