Shortest paths for disc obstacles

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3045, Issue , 2004, Pages 62-70

  Kim, Deok Soo ^a   Yu, Kwangseok ^a   Cho, Youngsong ^a   Kim, Donguk ^a   Yap, Chee ^b  

^a Hanyang University   (South Korea)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Convex hull; Dijkstra; Disc obstacles; Ellipse; Geodesic; Voronoi diagram

Indexed keywords

GEODESY; GRAPH THEORY;

CONVEX HULL; DIJKSTRA; DISC OBSTACLES; ELLIPSE; GEODESIC; VORONOI DIAGRAMS;

COMPUTATIONAL GEOMETRY;

EID: 31344457577     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24767-8_7     Document Type: Article

References (20)

1. Asano, T., Asano, T., Guibas, L., Hershberger, J., Imai, H.: Visibility of disjoint polyongs, Algorithmica, 1, (1986) 49-63.
2. Alexopoulos, C., Griffin, P.M.: Path planning for a mobile robot,IEEE Transactions on Systems, Man, and Cybernetics, Vol. 22, No. 2, (1992) 318-322.
3. Edelsbrunner, H., Guibas, L. J.: Topologically sweeping an arrangement, J. Comput. System Sci., 38, (1989) 165-194.
4. Gavrilova, M.: On a nearest-neighbor problem under Minkowski and power metrics for large data sets, The Journal of Supercomputing, 22, (2002) 87-98.
5. Ghosh, S.K., Mount, D.: An output sensitive algorithm for computing visibility graphs, SIAM J. Comput., 20, (1991) 888-910.
6. Kapoor, S., Maheswari, S.N.: Efficient algorithms for Euclidean shortest paths and visibility problems with polygonal obstacles, In Proc. 4th Annu. ACM Sympos. Comput. Geometry, (1988) 178-182.
7. Kim, D.-S., Kim, D., Sugihara, K.: Voronoi diagram of a circle set from Voronoi diagram of a point set: I. Topology, Computer Aided Geometric Design, Vol. 18 (2001) 541-562.
8. Kim, D.-S., Kim, D., Sugihara, K.: Voronoi diagram of a circle set from Voronoi diagram of a point set: II. Geometry, Computer Aided Geometric Design, Vol. 18 (2001) 563-585.
9. Mitchell, J.S.B.: Shortest paths among obstacles in the plane, In Proc. 9th Annu. ACM Sympos. Comput. Geom., (1993) 308-317.
10. Mucke, E. P., Saias, I., Zhu, B.: Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations, In Proc. 12th Annu. ACM Sympos. Comput. Geom., (1996) 274-283.
11. Okabe, A., Boots, B., Sugihara, K., Chiu, S. N.: Spatial Tessellations Concepts and Applications of Voronoi Diagrams, John Wiley & Sons, Chichester (2000)
12. Pocchiola, M., Vegter, G.: Computing visibility graphs via pseudo-triangulations, In Proc. 11th Annu. ACM Sympos. Comput. Geom., (1995) 248-257.
13. Pocchiola, M., Vegter, G.: Minimal tangent visibility graphs, Computational Geometry Theory and Applications, Vol. 6, (1996) 303-314.
14. Preparata, F.P., Shamos, M.I.: Computational Geometry: An Introduction, Springer-Verlag, New York (1985)
15. Rimon, E., Koditschek, D.E.: Exact robot navigation using artificial potential functions, IEEE Transactions on robotics and automation, Vol. 8, No. 5, (1992) 501-518.
16. Rohnert, H.: Shortest paths in the plane with convex polygonal obstacles, Inform. Process. Lett., Vol. 23, (1986) 71-76.
17. Rohnert, H.: Time and space efficient algorithms for shortest paths between convex polygons, Inform. Process. Lett., 27, (1988) 175-179.
18. Storer, J.A., Reif, J.H.: Shortest paths in the plane with polygonal obstacles, Journal of the Association for Computing Machinery, Vol. 41, No. 5, (1994) 982-1012.
19. Sudarshan, S., Rangan, C.P.: A fast algorithm for computing sparse visibility graphs, Algorithmica, Vol. 5, (1990) 201-214.
20. Sundar, S., Shiller, Z.: Optimal obstacle avoidance based on the Hamilton-Jacobi-Bellman equation, IEEE Transactions on robotics and automation, Vol. 13, No. 2, (1997) 305-310.