Abstract
This paper presents an approximation algorithm for finding minimum cost path between two points on the surface of a weighted polyhedron in 3D. It terminates in finite time. For a restricted class of polyhedron better approximation bound can be obtained.
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Agarwal, P.K., Har-Peled, S., Karia, M.: Computing approximate shortest paths on convex polytopes. Algorithmica 33, 227–242 (2002)
Aleksandrov, L., Lanthier, M., Maheshwari, A., Sack, J.-R.: An ε-approximation algorithm for weighted shortest paths on polyhedral surfaces. In: Arnborg, S. (ed.) SWAT 1998. LNCS, vol. 1432, pp. 11–22. Springer, Heidelberg (1998)
Aleksandrov, L., Maheshwari, A., Sack, J.-R.: Approximation algorithms for geometric shortest path problems. In: Proc. Symp. on Theory of Comput., pp. 286–295 (2000)
Aleksandrov, L., Maheshwari, A., Sack, J.-R.: An improved approximation algorithms for computing geometric shortest paths problems. In: Proc. Symp. on Foundations of Computing Theory, pp. 246–257 (2003)
Chen, J., Han, Y.: Shortest paths on a polyhedron. Int. J. on Computational Geometry and Applications 6, 127–144 (1996)
Dijkstra, E.W.: A note on two problems in connection with graphs. Numerical Mathematics 1, 267–271 (1959)
Kapoor, S.: Efficient computation of geodesic shortest paths. In: Symp. on Theory of Computing, pp. 770–779 (1999)
Lanthier, M., Maheswari, A., Sack, J.-R.: Approximating weighted shortest paths on polyhedral surfaces. Algorithmica 30, 527–562 (2001)
Mata, C., Mitchell, J.S.B.: A new algorithm for computing shortest paths in weighted planar subdivisions. In: Proc. 13th ACM Symp. Comput. Geom., pp. 264–273 (1997)
Mitchell, J.S.B., Mount, D.M., Papadimitrou, C.H.: Discrete geodesic problem. SIAM J. on Computing 16, 647–668 (1987)
Mitchell, J.S.B., Papadimitrou, C.H.: The weighted region problem: finding shortest paths through a weighted planar subdivision. J. of the Association for Computing Machinary 38, 18–73 (1991)
Papdimitriou, C.H.: An algorithm for shortest path motion in three dimension. Inform. Process. Lett. 20, 259–263 (1985)
Sack, J.R., Urrutia, J.: Handbook of computational geometry. North-Holland, Elsevier Science B. V., Netherlands (2000)
Sharir, M., Schorr, A.: On shortest paths in polyhedral space. SIAM J. Computing 15, 93–215 (1986)
Varadarajan, K.R., Agarwal, P.K.: Approximating shortest path on a non-convex polyhedron. SIAM J. Computing 30, 1321–1340 (2000)
Ziegelmann, M.: Constrained shortest paths and related problems, Ph.D. Thesis, Universitat des Saarlandes (Max-Plank Institut fur Informatik) (2001)
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Roy, S., Das, S., Nandy, S.C. (2004). A Practical Algorithm for Approximating Shortest Weighted Path between a Pair of Points on Polyhedral Surface. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_5
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DOI: https://doi.org/10.1007/978-3-540-24767-8_5
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