On geometric path query problems

International Journal of Computational Geometry and Applications

Volumn 11, Issue 6, 2001, Pages 617-645

  Chen, Danny Z ^a   Daescu, Ovidiu ^b   Klenk, Kevin S ^c  

^a University of Notre Dame   (United States)

^b The University of Texas at Dallas   (United States)

^c FORD MOTOR COMPANY   (United States)

Author keywords

Gateway; Geometric path query; Map; Optimal path; Visibility graph

Indexed keywords

EID: 0035730269     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218195901000675     Document Type: Article

References (46)

1. S. Arikati, D. Z. Chen, L. P. Chew, G. Das, M. Smid, and C. D. Zaroliagis. Planar spanners and approximate shortest path queries among obstacles in the plane. In J. Diaz and M. Serna, editors, Algorithms - ESA'96, volume 1136 of Lecture Notes in Computer Science, pages 514-528. Springer-Verlag, 25-27 Sept. 1996.
2. E. M. Arkin, R. Connelly, and J. S. B. Mitchell. On monotone paths among obstacles, with applications to planning assemblies. In Proceedings of the 5th Annual Symposium on Computational Geometry, pages 334-343. ACM, June 1989.
3. E. M. Arkin, J. S. B. Mitchell, and S. Suri. Logarithmic-time link path queries in a simple polygon. Internatational Journal of Computational Geometry & Applications, 5(4):369-395, 1995.
4. M. J. Atallah and D. Z. Chen. Parallel rectilinear shortest paths with rectangular obstacles. Computational Geometry: Theory and Applications, 1(2):79-113, 1991.
5. M. J. Atallah and D. Z. Chen. On parallel rectilinear obstacle-avoiding paths. Computational Geometry: Theory and Applications, 3:307-313, 1993.
6. O. Berkman and U. Vishkin. Finding level-ancestors in trees. Technical Report UMIACS-TR-91-9, University of Maryland, 1991.
7. B. Chazelle. An algorithm for segment dragging and its implementation. Algorithmica, 3:205-221, 1988.
8. D. Z. Chen. On the all-pairs Euclidean short path problem. In Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 292-301. ACM-SIAM, 22-24 Jan. 1995.
9. D. Z. Chen and K. S. Klenk. Erratum to "Rectilinear short path queries among rectangular obstacles". Information Processing Letters 57 (6) (25 March 1996) 313-319. Inf. Process. Lett., 60(2):105, 28 Oct. 1996.
10. D. Z. Chen and K. S. Klenk. Rectilinear short path queries among rectangular obstacles. Inf. Process. Lett., 57(6):313-319, 25 Mar. 1996.
11. D. Z. Chen, K. S. Klenk, and H.-Y. T. Tu. Shortest path queries among weighted obstacles in the rectilinear plane. SIAM J. Comput., 29(4):1223-1246, 2000.
12. Y.-J. Chiang and J. S. B. Mitchell. Two-point Euclidean shortest path queries in the plane. In Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM, 17-19 Jan. 1999.
13. Y.-J. Chiang, F. P. Preparata, and R. Tamassia. A unified approach to dynamic point location, ray shooting, and shortest paths in planar maps. In Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 44-53. ACM-SIAM, 25-27 Jan. 1993.
14. K. L. Clarkson. Approximation algorithms for shortest path motion planning. In Proceedings of the 19th Annual Symposium on the Theory of Computing, pages 56-65. ACM, 25-27 May 1987.
15. 3/2 n) time. Unpublished manuscript.
16. 2) time. In Proceedings of the 3rd Annual Symposium on Computational Geometry, pages 251-257. ACM, June 1987.
17. M. de Berg. On rectilinear link distance. Computational Geometry: Theory and Applications, 1:13-34, 1991.
18. H. Edelsbrunner, L. J. Guibas, and J. Stolfi. Optimal point location in a monotone subdivision. SIAM J. Comput., 15(2):317-340, May 1986.
19. H. ElGindy and P. Mitra. Orthogonal shortest route queries among axes parallel rectangular obstacles. International Journal of Computational Geometry & Applications, 4(1):3-24, 1994.
20. M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM, 34(3):596-615, July 1987.
21. M. T. Goodrich and R. Tamassia. Dynamic ray shooting and shortest paths via balanced geodesic triangulations. In Proceedings of the 9th Annual Symposium on Computational Geometry, pages 318-327. ACM, May 1993.
22. L. J. Guibas and J. Hershberger. Optimal shortest path queries in a simple polygon. In Proceedings of the 3rd Annual Symposium on Computational Geometry, pages 50-63. ACM, June 1987.
23. J. Hershberger. A new data structure for shortest path queries in a simple polygon. Inf. Process. Lett., 38(5):231-235, 14 June 1991.
24. J. Hershberger and S. Suri. Efficient computation of Euclidean shortest paths in the plane. In Proceedings of the 34th Annual Symposium on Foundations of Computer Science, pages 508-517. IEEE, 3-5 Nov. 1993.
25. J. Hershberger and S. Suri. An optimal algorithm for Euclidean shortest paths in the plane. SIAM J. Comput., 28(6):2215-2256, 1999.
26. M. Iwai, H. Suzuki, and T. Nishizeki. Shortest path algorithm in the plane with rectilinear polygonal obstacles. In Proc. of SIGAL Workshop, July 1994. In Japanese.
27. D. Kirkpatrick. Optimal search in planar subdivisions. SIAM J. Comput., 12(1):28-35, Feb. 1983.
28. D. T. Lee, C. D. Yang, and T. H. Chen. Shortest rectilinear paths among weighted obstacles. International Journal of Computational Geometry & Applications, 1(2):109-124, 1991.
29. D. T. Lee, C. D. Yang, and C. K. Wong. Rectilinear paths among rectilinear obstacles. Discrete Applied Mathematics, 70:185-215, 1996.
30. R. J. Lipton and R. E. Tarjan. Applications of a planar separator theorem. In Proceedings of the 18th Annual Symposium on Foundations of Computer Science, pages 162-170. IEEE, 31 Oct.-2 Nov. 1977.
31. R. J. Lipton and R. E. Tarjan. A separator theorem for planar graphs. In Proceedings of the Conference on Theoretical Computer Science, pages 1-10, Aug. 1977.
32. R. J. Lipton and R. E. Tarjan. Applications of a planar separator theorem. SIAM J. Comput., 9(3):615-627, Aug. 1980.
33. J. S. B. Mitchell. An optimal algorithm for shortest rectilinear paths among obstacles. Presented at the First Canadian Conference on Computational Geometry, Montreal, Canada, Aug. 1989.
34. J. S. B. Mitchell. Li shortest paths among polygonal obstacles in the plane. Algorithmica, 8:55-88, 1992.
35. J. S. B. Mitchell. Geometric shortest paths and network optimization. Handbook of Computational Geometry, J.-R. Sack and J. Urrutia (eds.), Elsevier Science, to appear, 2000.
36. J. S. B. Mitchell, G. Rote, and G. Woeginger. Minimum-link paths among obstacles in the plane. Algorithmica, 8:431-459, 1992.
37. P. Mitra and B. Bhattacharya. Efficient approximate shortest-path queries among isothetic rectangular obstacles. In F. Dehne, J.-R. Sack, N. Santoro, and S. Whitesides, editors, Algorithms and Data Structures: Third Workshop, WADS '93, Proceedings, volume 709 of Lecture Notes in Computer Science, pages 518-529. Springer-Verlag, 11-13 Aug. 1993.
38. M. Pocchiola and G. Vegter. Pseudotriangulations: Theory and applications. In Proceedings of the Twelfth Annual Symposium on Computational Geometry, pages 291-300. ACM, 24-26 May 1996.
39. M. Pocchiola and G. Vegter. The visibility complex. Internatational Journal of Computational Geometry & Applications, 6(3):279-308, 1996.
40. G. Reich. Finitely-oriented shortest paths in the presence of polygonal obstacles. Technical Report Bericht 39, Institut für Informatik, Universität Freiburg, Germany, Oct. 1991.
41. S. Sairam, R. F. Cohen, R. Tamassia, and J. S. Vitter. Fully dynamic techniques for reachability in planar sT-graphs. Technical Report CS-91-02, Department of Computer Science, Brown University, Providence, Rhode Island, 02912-1910, Dec. 1990.
42. S. Schuierer. An optimal data structure for shortest rectilinear path queries in a simple rectilinear polygon. Internatational Journal of Computational Geometry & Applications, 6(2):205-225, 1996.
43. G. T. Toussaint. Movable separability of sets. In G. T. Toussaint, editor, Computational Geometry, volume 2 of Machine Intelligence and Pattern Recognition, pages 335-375. Elsevier, Amsterdam, 1985.
44. P. Widmayer. On graphs preserving rectilinear shortest paths in the presence of obstacles. Annals of Operations Research, 33:557-575, 1991.
45. P. Widmayer, Y. F. Wu, and C. K. Wong. On some distance problems in fixed orientations. SIAM J. Comput., 16(4):728-746, Aug. 1987.
46. C.-D. Yang, D. T. Lee, and C. K. Wong. Rectilinear path problems among rectilinear obstacles revisited. SIAM J. Comput., 24(3):457-472, June 1995.