An optimal competitive strategy for walking in streets

SIAM Journal on Computing

Volumn 33, Issue 2, 2004, Pages 462-486

  Icking, Christian ^a   Klein, Rolf ^b   Langetepe, Elmar ^b   Schuierer, Sven ^c   Semrau, Ines ^d  

^a UNIVERSITY OF HAGEN   (Germany)

^b UNIVERSITY OF BONN   (Germany)

^c NOVARTIS PHARMA AG   (Switzerland)

^d UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Autonomous robot; Competitive strategy; Computational geometry; LR visibility; On line navigation; Path planning; Polygon; Street

Indexed keywords

ALGORITHMS; COMPUTER SCIENCE; MATHEMATICAL MODELS; MOBILE ROBOTS; MOTION PLANNING; PERFORMANCE; PROBLEM SOLVING; ROBOTICS;

COMPETITIVE STRATEGY; LR-VISIBILITY; ON-LINE NAVIGATION;

COMPUTATIONAL GEOMETRY;

EID: 2342638334     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539702419352     Document Type: Article

References (44)

1. S. ALPERN AND S. GAL, The Theory of Search, Games and Rendezvous, Kluwer Academic, Dordrecht, The Netherlands, 2002.
2. R. BAEZA-YATES, J. CULBERSON, AND G. RAWLINS, Searching in the plane, Inform, and Cornput., 106 (1993), pp. 234-252.
3. R. BELLMAN, Problem 63-9*, SIAM Rev., 5 (1963), p. 274.
4. P. BERMAN, On-line searching and navigation, in Online Algorithms: The State of the Art, A. Fiat and G. Woeginger, eds., Springer-Verlag, Berlin, 1998, pp. 232-241.
5. M. BLOM, S. O. KRUMKE, W. DE PAEPE, AND L. STOUGIE, The online-TSP against fair adversaries, INFORMS J. Comput., 13 (2001), pp. 138-148.
6. A. BLUM, P. RAGHAVAN, AND B. SCHIEBER, Navigating in unfamiliar geometric terrain, SIAM J. Comput., 26 (1997), pp. 110-137.
7. C. BRÖCKER AND A. LÓPEZ-ORTIZ, Position-independent street searching, in Algorithms and Data Structures (Vancouver, BC, 1999), Lecture Notes in Comput. Sci. 1663, Springer-Verlag, Berlin, 1999, pp. 241-252.
8. C. BRÖCKER AND S. SCHUIERER, Searching rectilinear streets completely, in Algorithms and Data Structures (Vancouver, BC, 1999), Lecture Notes in Comput. Sci. 1663, Springer-Verlag, Berlin, 1999, pp. 98-109.
9. S. CARLSSON AND B. J. NILSSON, Computing vision points in polygons, Algorithmica, 24 (1999), pp. 50-75.
10. G. DAS, P. HEFFERNAN, AND G. NARASIMHAN, LR-visibility in polygons, Comput. Geom. Theory Appl., 7 (1997), pp. 37-57.
11. P. DASGUPTA, P. P. CHAKRABARTI, AND S. C. DESARKAR, A new competitive algorithm for agent searching in unknown streets, in Foundations of Software Technology and Theoretical Computer Science (Hyderabad, 1996), Lecture Notes in Comput. Sci. 1180, Springer-Verlag, Berlin, 1996, pp. 147-155.
12. A. DATTA, C. A. HIPKE, AND S. SCHUIERER, Competitive searching in polygons: Beyond generalised streets, in Algorithms and Computations (Cairns, 1995), Lecture Notes in Comput. Sci. 1004, Springer-Verlag, Berlin, 1995, pp. 32-41.
13. A. DATTA AND C. ICKING, Competitive searching in a generalized street, in Proceedings of the 10th Annual ACM Symposium on Computational Geometry, ACM Press, New York, 1994, pp. 175-182.
14. A. DATTA AND C. ICKING, Competitive searching in a generalized street, Comput. Geom. Theory Appl., 13 (1999), pp. 109-120.
15. A. FIAT AND G. WOEGINGER, EDS., Online Algorithms: The State of the Art, Lecture Notes in Comput. Sci. 1442, Springer-Verlag, Berlin, 1998.
16. S. GAL, Search Games, Math. Sci. Engrg. 149, Academic Press, New York, 1980.
17. S. K. GHOSH AND S. SALUJA, Optimal on-line algorithms for walking with minimum number of turns in unknown streets, Comput. Geom. Theory Appl., 8 (1997), pp. 241-266.
18. F. HOFFMANN, C. ICKING, R. KLEIN, AND K. KRIEGEL, The polygon exploration problem, SIAM J. Comput., 31 (2001), pp. 577-600.
19. C. ICKING, Motion and Visibility in Simple Polygons, Ph.D. thesis, Department of Computer Science, FernUniversität Hagen, Germany, 1994.
20. C. ICKING, R. KLEIN, AND E. LANGETEPE, Searching for the Kernel of a Polygon: A Competitive Strategy Using Self-approaching Curves, Tech. Rep. 211, Department of Computer Science, FernUniversität Hagen, Germany, 1997.
21. C. TOKING, R. KLEIN, AND E. LANGETEPE, An optimal competitive strategy for walking in streets, in Proceedings of the 16th Symposium on Theoretical Aspects in Computer Science, Lecture Notes in Comput. Sci. 1563, Springer-Verlag, Berlin, 1999, pp. 110-120.
22. C. ICKING, R. KLEIN, AND L. MA, How to look around a corner, in Proceedings of the 5th Canadian Information Processing Society Congress, University of Waterloo, Waterloo, Canada, 1993, pp. 443-448.
23. C. ICKING, A. LÓPEZ-ORTIZ, S. SCHUIERER, AND I. SEMRAU, Going Home through an Unknown Street, Tech. Rep. 228, Department of Computer Science, FernUniversität Hagen, Germany, 1998.
24. R. KLEIN, Walking an unknown street with bounded detour, in Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1991, pp. 304-313.
25. R. KLEIN, Walking an unknown street with bounded detour, Comput. Geom. Theory Appl., 1 (1992), pp. 325-351.
26. J. M. KLEINBERG, On-line search in a simple polygon, in Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms (Arlington, VA, 1994), ACM Press, New York, 1994, pp. 8-15.
27. E. KRANAKIS AND A. SPATHARIS, Almost optimal on-line search in unknown streets, in Proceedings of the 9th Canadian Conference on Computational Geometry, Kingston, ON, Canada, 1997, pp. 93-99.
28. A. LÓPEZ-ORTIZ, On-line Target Searching in Bounded and Unbounded Domains, Ph.D. thesis, University of Waterloo, Waterloo, Canada, 1996.
29. A. LÓPEZ-ORTIZ AND S. SCHUIERER, Going home through an unknown street, in Algorithms and Data Structures (Kingston, ON, 1995), Lecture Notes in Comput. Sci. 955, Springer-Verlag, Berlin, 1995, pp. 135-146.
30. A. LÓPEZ-ORTIZ AND S. SCHUIERER, Generalized streets revisited, in Proceedings of the 4th Annual European Symposium on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, Berlin, 1996, pp. 546-558.
31. A. LÓPEZ-ORTIZ AND S. SCHUIERER, Walking streets faster, in Proceedings of the 5th Scandinavian Workshop on Algorithm Theory, Lecture Notes in Comput. Sci. 1097, Springer-Verlag, Berlin, 1996, pp. 345-356.
32. A. LÓPEZ-ORTIZ AND S. SCHUIERER, The Exact Cost of Exploring Streets with CAB, tech. rep., Institut für Informatik, Universität Freiburg, Germany, 1998.
33. A. LÓPEZ-ORTIZ AND S. SCHUIERER, Lower Bounds for Searching on Generalized Streets, tech. rep., University of New Brunswick, Canada, 1998.
34. A. LÓPEZ-ORTIZ AND S. SCHUIERER, Online parallel heuristics and robot searching under the competitive framework, in Proceedings of the 8th Scandinavian Workshop on Algorithm Theory, Lecture Notes in Comput. Sci. 2368, Springer-Verlag, Berlin, 2002, pp. 260-269.
35. J. S. B. MITCHELL, Geometric shortest paths and network optimization, in Handbook of Computational Geometry, J.-R. Sack and J. Urrutia, eds., North-Holland, Amsterdam, 2000, pp. 633-701.
36. T. OTTMANN, S. SCHUIERER, AND C. A. HIPKE, Kompetitive Analyse für Online-Algorithmen: Eine kommentierte Bibliographie, Tech. Rep. 61, Institut für Informatik, Universität Freiburg, Germany, 1994.
37. N. S. V. RAO. S. KARETI, W. SHI, AND S. S. IYENGAR, Robot Navigation in Unknown Terrains: Introductory Survey of Non-heuristic Algorithms, Tech. Rep. ORNL/TM-12410, Oak Ridge National Laboratory, Oak Ridge, TN, 1993.
38. J.-R. SACK AND J. URRUTIA, EDS., Handbook of Computational Geometry, North-Holland, Amsterdam, 2000.
39. S. SCHUIERER, Lower bounds in on-line geometric searching, in Proceedings of the 11th International Symposium on Fundamentals of Computation Theory, Lecture Notes in Comput. Sci. 1279, Springer-Verlag, Berlin, 1997, pp. 429-440.
40. S. SCHUIERER AND I. SEMRAU, An optimal strategy for searching in unknown streets, in Proceedings of the 16th Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Comput. Sci. 1563, Springer-Verlag, Berlin, 1999, pp. 121-131.
41. R. SEIDEL, personal communications via Rolf Klein, 1999.
42. I. SEMRAU, Analyse und experimentelle Untersuchung von Strategien zum Finden eines Ziels in Straβenpolygonen, diploma thesis, FernUniversität Hagen, Germany, 1996.
43. D.D. SLEATOR AND R.E. TARJAN, Amortized efficiency of list update and paging rules, Comm. ACM, 28 (1985), pp. 202-208.
44. L. H. TSENG, P. HEFFERNAN, AND D. T. LEE, Two-guard workability of simple polygons, Internat. J. Comput. Geom. Appl., 8 (1998), pp. 85-116.