Fréchet distance problems in weighted regions

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

Volumn 5878 LNCS, Issue , 2009, Pages 97-111

  Cheung, Yam Ki ^a   Daescu, Ovidiu ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

FACTOR APPROXIMATION ALGORITHMS; LINE SEGMENT; PLANAR SUBDIVISION; POLYGONAL CURVE; SHORTEST PATH; TWO-POINT; WEIGHTED REGIONS;

COMPUTATION THEORY;

APPROXIMATION ALGORITHMS;

EID: 75649128001     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-10631-6_12     Document Type: Conference Paper

References (21)

1. Aleksandrov, L., Djidjev, H.N., Guo, H., Maheshwari, A., Nussbaum, D., Sack, J.: Approximate shortest path queries on weighted polyhedral surfaces. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 98-109. Springer, Heidelberg (2006)
2. Aleksandrov, L., Maheshwari, A.A., Sack, J.R.: Approximation algorithms for geometric shortest path problems. In: Proc. 32nd Annual ACM Symposium on Theory of Computing, pp. 286-295 (2000)
3. Aleksandrov, L., Maheshwari, A., Sack, J.: Determining approximate shortest paths on weighted polyhedral surfaces. Journal of the ACM 52(1), 25-53 (2005)
4. Alt, H., Godau, M.: Computation the Fréchet distance between two polygonal curves. International Journal of Computational Geometry and Applications 5, 75-91 (1995)
5. Amato, N.M., Goodrich, M.T., Ramos, E.A.: Computing the arrangement of curve segments: Divide-and-conquer algorithms via sampling. In: Proc. 11th Annual CAM-SIAM Symposium on Discrete Algorithms, pp. 705-706 (2000)
6. Buchin, K., Buchin, M., Wenk, C.: Computing the Fréchet distance between simple polygons in polynomial time. In: Proc. 22nd Symposium on Computational Geometry, pp. 80-87 (2006)
7. Buchin, K., Buchin, M., Wang, Y.: Exact partial curve matching under the Fréchet distance. In: Proc. ACM-SIAM Symposium on Discrete Algorithms (to appear, 2009)
8. Chambers, E.W., De Verdière, C. É., Erickson, J., Lazard, S., Lazarus, F., Thite, S.: Walking your dog in the woods in polynomial time. In: Proc. 24th Annual ACM Symposium on Computational Geometry, pp. 101-109 (2008)
9. Chen, D.Z., Daescu, O., Hu, X., Wu, X., Xu, J.: Determining an optimal penetration among weighted regions in two and three dimensions. J. combinat. Optim. 5(1), 59-79 (2001)
10. Cheng, S.W., Na, H.S., Vigneron, A., Wang, Y.: Approximate shortest paths in anisotropic regions. In: Proc. 18th annual ACM-SIAM symposium on Discrete algorithms, pp. 766-774 (2007)
11. Cheng, S.W., Na, H.S., Vigneron, A., Wang, Y.: Querying approximate shortest paths in anisotropic regions. In: Proc. 23rd annual symposium on Computational geometry, pp. 84-91 (2005)
12. Clarkson, K.L.: Approximation algorithms for shortest path motion planning. In: Proc. 19th Annual ACM Symposium on Theory of Computing, pp. 56-65 (1987)
13. Collins, G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 134-183. Springer, Heidelberg (1975)
14. Cook IV, A.F., Wenk, C.: Geodesic Fréchet distance inside a simple polygon. In: Proc. 25th International Symposium on Theoretical Aspects of Computer Science, pp. 193-204 (2008)
15. Eiter, T., Mannila, H.: Computing discrete Fréchet distance. Technical Report CD-TR 94/64, Information Systems Department, Technical University of Vienna (1994)
16. Fréchet, M.: Sur quelques points du calcul fonctionnel. Rendiconti del Circolo Mathematico di Palermo 22, 1-74 (1906)
17. Maheshwari, A., Yi, J.: On computing Fréchet distance of two paths on a convex polyhedron. In: Proc. 21st European Workshop on computational Geometry, pp. 41-44 (2005)
18. Mitchell, J.S.B., Papadimitriou, C.H.: The weighted region problem: Finding shortest paths through a weighted planer subdivision. Journal of the ACM 38(1), 18-73 (1991)
19. Rote, G.: Computing the Fréchet distance between piecewise smooth curves. Technical Report, ECGTR-241108-01 (2005)
20. Sun, Z., Reif, J.H.: On finding approximate optimal path in weighted regions. Journal of Algorithms 58(1), 1-32 (2006)
21. Beer-Lambert law. Wikipedia, http://en.wikipedia.org/wiki/BeerLambert-law