Abstract
In this paper we study the problem of a robot searching for a visually recognizable target in an unknown simple polygon. We present two algorithms. Both work for arbitrarily oriented polygons. The search cost is proportional to the distance traveled by the robot. We use competitive analysis to judge the performance of our strategies. The first one is a simple modification of Dijkstra’s shortest path algorithm and achieves a competitive ratio of 2n − 7 where n is the number of vertices of the polygon. The second strategy achieves a competitive ratio of 1 + 2 
(2k)2k/(2k−1)\(^{\rm 2{\it k}-1}\) if the polygon is k-spiral. This can be shown to be optimal. It is based on an optimal algorithm to search in geometric trees which is also presented in this paper.
Consider a geometric tree with m leaves and a target hidden somewhere in the tree. The target can only be detected if the robot reaches the location of the target. We provide an algorithm that achieves a competitive ratio of 1 + 2m m/(m−1)m − 1 and show its optimality.
This research is supported by the DFG-Project ”Diskrete Probleme”, No. Ot 64/8-2.
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References
Baeza-Yates, R., Culberson, J., Rawlins, G.: Searching in the plane. Information and Computation 106, 234–252 (1993)
Datta, A., Hipke, C., Schuierer, S.: Competitive searching in polygons— beyond generalized streets. In: Staples, J., Katoh, N., Eades, P., Moffat, A. (eds.) ISAAC 1995. LNCS, vol. 1004, pp. 32–41. Springer, Heidelberg (1995)
Datta, A., Icking, C.: Competitive searching in a generalized street. In: Proc. 10th Annu. ACM Sympos. Comput. Geom., pp. 175–182 (1994)
Gal, S.: Search Games. Academic Press, London (1980)
Icking, C.: Motion and Visibility in Simple Polygons. PhD thesis, Fernuniversit ät Hagen (1994)
Klein, R.: Walking an unknown street with bounded detour. Comput. Geom. Theory Appl. 1, 325–351 (1992)
Kleinberg, J.M.: On-line search in a simple polygon. In: Proc. of 5th ACMSIAM Symp. on Discrete Algorithms, pp. 8–15 (1994)
Klein, R.: Algorithmische Geometrie. Addison-Wesley, Reading (1997)
López-Ortiz, A., Schuierer, S.: Generalized streets revisited. In: Diaz, J., Serna, M. (eds.) ESA 1996. LNCS, vol. 1136, pp. 546–558. Springer, Heidelberg (1996)
López-Ortiz, A., Schuierer, S.: Position-independent near optimal searching and on-line recognition in star polygons. In: Rau-Chaplin, A., Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 1997. LNCS, vol. 1272, pp. 284–296. Springer, Heidelberg (1997)
Papadimitriou, C.H., Yannakakis, M.: Shortest paths without a map. Theoretical Computer Science 84(1), 127–150 (1991)
Semrau, I.: Personal communications (1997)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28, 202–208 (1985)
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Schuierer, S. (1999). On-Line Searching in Simple Polygons. In: Christensen, H.I., Bunke, H., Noltemeier, H. (eds) Sensor Based Intelligent Robots. Lecture Notes in Computer Science(), vol 1724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10705474_12
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DOI: https://doi.org/10.1007/10705474_12
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