An efficient algorithm for Euclidean shortest paths among polygonal obstacles in the plane

Discrete and Computational Geometry

Volumn 18, Issue 4, 1997, Pages 377-383

  Kapoor, S ^a   Maheshwari, S N ^a   Mitchell, J S B ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY DELHI   (India)

^b Stony Brook University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031502943     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009323     Document Type: Article

References (23)

1. T. Asano, T. Asano, L. Guibas, J. Hershberger, and H. Imai, Visibility of disjoint polygons, Algorithmica 1 (1986), 49-63.
2. R. Bar-Yehuda and B. Chazelle, Triangulating disjoint Jordan chains, Internat. J. Comput. Geom. Appl. 4 (1994), 475-481.
3. M. Fredman and R. Tarjan, Fibonacci heaps and their uses in improved network optimization problems, J. Assoc. Comput. Mach. 34 (1987), 596-615.
4. S.K. Ghosh and D.M. Mount, An output-sensitive algorithm for computing visibility graphs, SIAM J. Comput. 20 (1991), 888-910.
5. L.J. Guibas and J. Hershberger, Optimal shortest path queries in a simple polygon, J. Comput. System Sci. 39 (1989), 126-152.
6. L.J. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. Tarjan, Linear time algorithms for visibility and shortest path problems inside triangulated simple polygons, Algorithmica 2 (1987), 209-233.
7. J. Hershberger and S. Suri, On computing Euclidean shortest paths in the plane, Proc. 34th Annual IEEE Symposium on Foundations of Computer Science, 1993, pp. 508-517.
8. J. Hershberger and S. Suri, An optimal-time algorithm for Euclidean shortest paths in the plane, Manuscript, Washington University, 1995.
9. S. Hertel and K. Mehlhorn, Fast triangulation of the plane with respect to simple polygons, Inform. Control 64 (1985), 52-76.
10. S. Kapoor and S.N. Maheshwari, Efficient algorithms for Euclidean shortest path and visibility problems with polygonal obstacles, Proc. Fourth Annual ACM Symposium on Computational Geometry, 1988, pp. 172-182.
11. S. Kapoor and S.N. Maheshwari, An efficient algorithm for Euclidean shortest path with polygonal obstacles, Technical Report, Dept. of Computer Science and Engineering, Indian Institute of Technology, Hauz Khas, New Delhi, 1994.
12. D.T. Lee and F.P. Preparata, Euclidean shortest paths in the presence of rectilinear boundaries, Networks 14 (1984), 393-410.
13. J.S.B. Mitchell, A new algorithm for shortest paths among obstacles in the plane, Ann. Math. Artificial Intel. 3 (1991), 83-106.
14. J.S.B. Mitchell, Shortest paths among obstacles in the plane, Internat. J. Comput. Geom. Appl. 6 (1996), 309-332.
15. J.S.B. Mitchell, Shortest paths and networks, in CRC Handbook of Discrete and Computational Geometry (E. Goodman and J. O'Rourke, eds.), CRC Press, Boca Raton, FL, 1997, pp. 445-466.
16. J.S.B. Mitchell and S. Suri, Separation and approximation of polyhedral surfaces, Comput. Geom. Theory Appl. 5 (1995), 95-114.
17. M.H. Overmars and E. Welzl, New methods for computing visibility graphs, Proc. Fourth Annual ACM Symposium on Computational Geometry, 1988, pp. 164-171.
18. M. Pocchiola and G. Vegter, The visibility complex, Internat. J. Comput. Geom. Appl. 6 (1996), 279-308.
19. H. Rohnert, Shortest paths in the plane with convex polygonal obstacles, Inform. Process. Lett. 23 (1986), 71-76.
20. H. Rohnert, A new algorithm for shortest paths avoiding convex polygonal obstacles, Report A86/02, Fachber. Inform., Univ. Saarlandes, Saarbrücken, 1986.
21. M. Sharir and A. Schorr, On shortest paths in polyhedral spaces, SIAM J. Comput. 1 (1986), 193-215.
22. J.A. Storer and J.H. Reif, Shortest paths in the plane with polygonal obstacles, J. Assoc. Comput. Mach. 41 (1994), 982-1012.
23. 2) time, Inform. Process. Lett. 20 (1985), 167-171.