Computing approximate shortest paths on convex polytopes

Algorithmica (New York)

Volumn 33, Issue 2, 2002, Pages 227-242

  Agarwal, P K ^a   Har Peled, S ^b   Karia, M ^c  

^a Duke University   (United States)

^b University of Illinois at Urbana Champaign   (United States)

^c Trilogy Software Inc   (United States)

Author keywords

Approximation algorithms; Covex polytopes; Path planning

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATION THEORY; GRAPH THEORY; HEURISTIC METHODS;

WATER FLOW ANALYSIS;

MOTION PLANNING;

EID: 0141922689     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-001-0111-x     Document Type: Article

References (33)

1. [AHPK] P. K. Agarwal, S. Har-Peled, and M. Karia. Shortest path-demo program, http://www.cs.duke. edu/-sariel/papers/99/nav/nav.html, 1999.
2. [AHPSV] P. K. Agarwal, S. Har-Peled, M. Sharir, and K. R. Varadarajan. Approximate shortest paths on a convex polytope in three dimensions. J. Assoc. Comput. Mach., 44:567-584, 1997.
3. [ALMS] L. Aleksandrov, M. Lanthier, A. Maheshwari, and J.-R. Sack. An ε-approximation algorithm for weighted shortest paths on polyhedral surfaces. In Proc. 6th Scand. Workshop Algorithm Theory, volume 1432 of Lecture Notes Computer Science, pages 11-22. Springer-Verlag, Berlin, 1998.
4. [AMS] L. Aleksandrov, A. Maheshwari, and J.-R. Sack. Approximation algorithms for geometric shortest path problems. In Proc. 32nd Annu. ACM Sympos. Theory Comput., pages 286-295, 2000.
5. [AR] R. Alexander and N. Rowe. Path planning by optimal-path-map construction for homogeneous-cost two-dimensional regions. In Proc. IEEE Internat. Conf. Robot. Automat., 1990.
6. [CH] J. Chen and Y. Han. Shortest paths on a polyhedron. In Proc. 6th Annu. ACM Sympos. Comput. Geom., pages 360-369, 1990.
7. [DK] D. P. Dobkin and D. G. Kirkpatrick. A linear algorithm for determining the separation of convex polyhedra. J. Algorithms, 6:381-392, 1985.
8. [Do] D. H. Douglas. Least cost path in geographic information systems. Research Note No. 61, Department of Geography, University of Ottawa, Ottawa, Ontario, Aug. 1993.
9. [Du] R. M. Dudley. Metric entropy of some classes of sets with differentiable boundaries. J. Approx. Theory, 10(3):227-236, 1974.
10. [EGS] H. Edelsbrunner, L. J. Guibas, and J. Stolfi. Optimal point location in a monotone subdivision. SIAM J. Comput., 15(2):317-340, 1986.
11. [G] M. Gardner, editor. Second Scientific American Book of Mathematical Puzzles and Diversions. University of Chicago Press, Chicago, IL, 1987.
12. [HP] S. Har-Peled. Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions. Discrete Comput. Geom., 21:216-231, 1999.
13. [HW] G. Hardy and E. Wright. The Theory of Numbers, 4th edition. Oxford University Press, London, 1965.
14. [HG] P. Heckbert and M. Garland. Survey of polygonal surface simplification algorithms. Technical Report, Department of Computer Science, Carnegie Mellan University, Pittsburgh, PA, 1997. http://www.cs.cmu.edu/-garland/Papers/simp.pdf.
15. 3. Comput. Geom. Theory Appl., 10(1):31-46, 1998.
16. [J] P. Johansson. On a weighted distance model for injection moulding. Linköping Studies in Science and Technology, Thesis No. 604 LiU-TEK-LIC-1997:05, Division of Applied Mathematics, Linköping University, Linköping, Feb. 1997.
17. [K] S. Kapoor. Efficient computation of geodesic shortest paths. In Proc. 31st Annu. ACM Sympos. Theory Comput., pages 770-779, 1999.
18. [KSR1] M. Kindl, M. Shing, and N. Rowe. A stochastic approach to the weighted-region problem, I: The design of the path annealing algorithm. Technical report, Computer Science, U.S. Naval Postgraduate School, Monterey, CA, 1991.
19. [KSR2] M. Kindl, M. Shing, and N. Rowe. A stochastic approach to the weighted-region problem, II: Performance enhancement techniques and experimental results. Technical report, Computer Science, U.S. Naval Postgraduate School, Monterey, CA, 1991.
20. [LMS] M. Lanthier, A. Maheshwari, and J.-R. Sack. Approximating weighted shortest paths on polyhedral surfaces. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 274-283, 1997.
21. [L] M. J. Longtin. Cover and concealment in ModSAF. In Proc. 4th Conf. Comput. Generated Forces Behav. Represent., pages 239-247, 1994.
22. [LM] M. J. Longtin and D. Megherbi. Concealed routes in ModSAF. In Proc. 5th Conf. Comput. Generated Forces Behav. Represent., pages 305-313, 1995.
23. [MM] C. Mata and J. S. B. Mitchell. A new algorithm for computing shortest paths in weighted planar subdivisions. In Proc. 13th Annu. ACM Sympos. Comput. Geom., pages 264-273, 1997.
24. [MN] K. Mehlhorn and S. Näher. LEDA: A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge, 1999.
25. [M] J. S. B. Mitchell. An algorithmic approach to some problems in terrain navigation. In Autonomous Mobile Robots: Perception, Mapping, and Navigation (S. S. Iyengar and A. Elfes, eds.), pages 408-427. IEEE Computer Society Press, Los Alamitos, CA, 1991.
26. [MMP] J. S. B. Mitchell, D. M. Mount, and C. H. Papadimilriou. The discrete geodesic problem. SIAM J. Comput., 16:647-668, 1987.
27. [P1] C. H. Papadimitriou. Efficient search for rationals. Inform. Process. Lett., 8(1):1-4, 1979.
28. [P2] C. H. Papadimitriou. An algorithm for shortest-path motion in three dimensions. Inform. Process. Lett., 20:259-263, 1985.
29. [RRZM] R. F. Richbourg, N. C. Rowe, M. J. Zyda, and R. McGhee. Solving global two-dimensional routing problems using Snell's law. In Proc. IEEE Internat. Conf. Robot. Automat., pages 1631-1636, 1987.
30. [S] S. Schirra. Robustness and precision issues in geometric computation. In Handbook of Geometric Computation (J.-R. Sack and J. Urrutia, eds.), pages 597-622. North-Holland, Amsterdam, 2000.
31. [SS] M. Sharir and A. Schorr. On shortest paths in polyhedral spaces. SIAM J. Comput., 15:193-215, 1986.
32. [VA] K. R. Varadarajan and P. K. Agarwal. Approximating shortest paths on a nonconvex polyhedron. SIAM J. Computing, 30:1321-1340, 2001.
33. [W] W. Warntz. Transportation, social physics, and the law of refraction. Prof. Geog., 9(4):2-7, 1957.