Proximity Problems for Points on a Rectilinear Plane with Rectangular Obstacles

Algorithmica (New York)

Volumn 17, Issue 3, 1997, Pages 281-307

  Guha, S ^a   Suzuki, I ^a  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

Computational geometry; Minimal spanning tree; Nearest neighbors; Obstacles; Rectilinear metric; Voronoi diagram

Indexed keywords

EID: 0003658330     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02523193     Document Type: Article

References (21)

1. B. Aronov, On the geodesic Voronoi diagram of point sites in a simple polygon, Algorithmica 4 (1989), 109-140.
2. M. J. Atallah, D. Chen, Parallel rectilinear shortest paths with rectangular obstacles, Proc. ACM Symp. on Parallel Algorithms and Architectures, 1990, pp. 270-279. Also in Comput. Geom. Theory Appl. 1 (1991), 79-113.
3. M. J. Atallah, D. Chen, Parallel rectilinear shortest paths with rectangular obstacles, Proc. ACM Symp. on Parallel Algorithms and Architectures, 1990, pp. 270-279. Also in Comput. Geom. Theory Appl. 1 (1991), 79-113.
4. J. L. Bentley, M. I. Shamos, Divide-and-conquer in multidimensional space, Proc. ACM Symp. on Theory of Computing, 1976, pp. 220-230.
5. D. Cheriton, R. E. Tarjan, Finding minimum spanning trees, SIAM J. Comput. 5 (1976), 724-742.
6. 2) time, Proc. ACM Symp. on Computational Geometry, 1987, pp. 251-257.
7. P. J. de Rezende, D. T. Lee, Y. F. Wu, Rectilinear shortest paths with rectangular barriers, Proc. ACM Symp. on Computational Geometry, 1985, pp. 204-213. Also in Discrete Comput. Geom. 4 (1989), 41-53.
8. P. J. de Rezende, D. T. Lee, Y. F. Wu, Rectilinear shortest paths with rectangular barriers, Proc. ACM Symp. on Computational Geometry, 1985, pp. 204-213. Also in Discrete Comput. Geom. 4 (1989), 41-53.
9. D. Dobkin, R. Lipton, On the complexity of computations under varying sets of primitives, J. Comput. System Sci. 18 (1979), 86-91.
10. S. Guha, Parallel Algorithms for Polygonal and Rectilinear Geometry, Ph.D. Thesis, Computer Science and Engineering, University of Michigan, Ann Arbor, MI, 1991.
11. L. Guibas, J. Hershberger, D. Leven, M. Sharir, R. Tarjan, Linear-time algorithms for visibility and shortest path problems inside a triangulated simple polygons, Algorithmica 2 (1987), 209-233.
12. D. G. Kirkpatrick, Optimal search in planar subdivision, SIAM J. Comput. 12 (1983), 28-35.
13. R. C. Larson, V. O. Li, Finding minimum rectilinear distance paths in the presence of barriers, Networks 11 (1981), 285-304.
14. p-metric, J. Assoc. Comput. Mach. 27 (1980), 604-618.
15. D. T. Lee, C. D. Yang, T. H. Chen, Shortest rectilinear paths among weighted obstacles, Internat. J. Comput. Geom. Appl. 1 (1991), 109-204.
16. 1 shortest paths among polygonal obstacles in the plane, Algorithmica 8 (1992), 55-88.
17. F. P. Prearata, M. I. Shamos, Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.
18. M. I. Shamos, D. Hoey, Closest-point problems, Proc. IEEE Symp. on Foundations of Computer Science, 1975, pp. 151-162.
19. P. Widmayer, Y. F. Wu, C. K. Wong, On some distance problems in fixed orientations, SIAM J. Comput. 16 (1987), 728-246.
20. Y. F. Wu, P. Widmayer, M. D. F. Schlag, C. K. Wong, Rectilinear shortest paths and minimum spanning trees in the presence of rectilinear obstacles, IEEE Trans. Comput. 36 (1987), 321-331.
21. C. D. Yang, D. T. Lee, C. K. Wong, On bends and lengths of rectilinear paths: a graph-theoretic approach, Internat. J. Comput. Geom. Appl. 2 (1992), 61-74.