Abstract
In this paper we describe an algorithm based on the idea of the direct multiple shooting method for solving approximately 2D geometric shortest path problems (introduced by An et al. in Journal of Computational and Applied Mathematics, 244 (2103), pp. 67-76). The algorithm divides the problem into suitable sub-problems, and then solves iteratively sub-problems. A so-called collinear condition for combining the sub-problems was constructed to obtain an approximate solution of the original problem. We discuss here the performance of the algorithm. In order to solve the sub-problems, a triangulation-based algorithm is used. The algorithms are implemented by C++ code. Numerical tests for An et al.’s algorithm are given to show that it runs significantly in terms of run time and memory usage.
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-662-45947-8_8
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
An, P.T., Hai, N.N., Hoai, T.V.: Direct multiple shooting method for solving approximate shortest path problems. Journal of Computational and Applied Mathematics 244, 67–76 (2103)
An, P.T., Hoai, T.V.: Incremental convex hull as an orientation to solving the shortest path problem. International Journal of Information and Electronics Engineering 2(5), 652–655 (2012)
Aleksandrov, L., Maheshwari, A., Sack, J.-R.: Approximation algorithms for geometric shortest path problems, In: Proceedings of the 32nd ACM-STOC (Symposium on Theory of Computing), pp. 286–295, Portland, Oregon (2000)
Book, H.G., Plitt, K.J.: A multiple shooting method for direct solution optimal control problems. In: Proceedings of the 9th IFAC World Progress, pp. 225–236. Pergamon Press, Budapest (1984)
Chazelle, B., Guibas, L.: Visibility and intersection problems in plane geometry. In: Proceedings of 1st ACM Symposium on Computational Geometry, pp. 135–146 (1985)
Clarkson, K.: Approximation algorithms for shortest path motion planning. In: Proceedings of the 19th Annual ACM Symposium on Theory of Computing, pp. 56–65, New York (1987)
Demyen, D., Buro, M.: Efficient triangulation-based pathfinding. In: Proceedings of the 21st National Conference on Artificial Intelligence and the Eighteenth Innovative Applications of Artificial Intelligence Conference, pp. 942–947, Boston, Massachusetts, USA (2006)
Kallmann, M.: Path planning in triangulation. In: Proceedings of the Workshop on Reasoning. Representation, and Learning in Computer Games, International Joint Conference on Artificial Intelligence (IJCAI), pp. 49–54, Edinburgh, Scotland (2005)
O’Rourke, J.: Computational Geometry in C, 2nd edn. Cambridge University Press (1998)
Lee, T., Preparata, F.P.: Euclidean shortest paths in the presence of rectilinear barriers. Networks 14, 393–410 (1984)
Mitchell, J.S.B.: Geometric shortest paths and network optimization. In: Sack, J.R., Urrutia, J. (eds.) Handbook of Computational Geometry, pp. 633–701. Elsevier Science B. V. (2000)
Sharir, M., Schorr, A.: On shortest paths in polyhedral spaces. SIAM Journal on Computing 15(1), 193–215 (1986)
Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis, 3rd edn. Springer, New York (2002)
Toussaint, G.T.: Computing geodesic properties inside a simple polygon. Revue D’Intelligence Artificielle 3, 9–42 (1989)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
An, P.T., Hai, N.N., Hoai, T.V., Trang, L.H. (2014). On the Performance of Triangulation-Based Multiple Shooting Method for 2D Geometric Shortest Path Problems. In: Hameurlain, A., Küng, J., Wagner, R., Dang, T., Thoai, N. (eds) Transactions on Large-Scale Data- and Knowledge-Centered Systems XVI. Lecture Notes in Computer Science(), vol 8960. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45947-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-662-45947-8_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-45946-1
Online ISBN: 978-3-662-45947-8
eBook Packages: Computer ScienceComputer Science (R0)