On the Performance of Triangulation-Based Multiple Shooting Method for 2D Geometric Shortest Path Problems

  • Phan Thanh An
  • Nguyen Ngoc Hai
  • Tran Van Hoai
  • Le Hong TrangEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8960)


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.


Approximate algorithm Multiple shooting method Memory usage Run time Shortest path 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Phan Thanh An
    • 1
    • 2
  • Nguyen Ngoc Hai
    • 3
  • Tran Van Hoai
    • 4
  • Le Hong Trang
    • 1
    • 5
    Email author
  1. 1.Instituto Superior TécnicoCEMATLisboaPortugal
  2. 2.Institute of MathematicsHanoiVietnam
  3. 3.Department of MathematicsInternational University, Vietnam National UniversityThu Duc, Ho Chi Minh CityVietnam
  4. 4.Faculty of Computer Science and EngineeringHCMC University of TechnologyHo Chi Minh CityVietnam
  5. 5.Faculty of Information TechnologyVinh UniversityVinhVietnam

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