Advertisement

How to generate realistic sample problems for network optimization

  • Masao Iri
Session 7: Invited Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)

Abstract

Experimental tests are probably the most direct way of evaluating the performance of computer algorithms and of appealing to their users. However, there seems to be no apparent agreement regarding how to generate sample problems for the test. Commonly used random generation, for example, has several problems since that solely produces those instances which follow truly even distribution and then which do not look like “real” samples we actually encounter in the world of actuality. In this paper, we discuss what kind of properties are significant for proper generation of sample problems from a practical-mathematical point of view. Our attention is focussed mainly on the network optimization problems.

Keywords

Road Network Random Graph Voronoi Diagram Sample Problem Theoretical Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. Asano, M. Edahiro, H. Imai, M. Iri and K. Murota: Practical use of bucketing techniques in computational geometry. In: G. T. Toussaint (ed.): Computational Geometry, Elsevier (North Holland), pp. 153–195 (1985)Google Scholar
  2. 2.
    P. Erdös and A. Rényi: On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, Vol. 5A, pp. 17–61 (1960)Google Scholar
  3. 3.
    P. Erdös and A. Rényi: On random graphs I. Publicationes Mathematicae (Debrecen), Vol. 6, pp. 290–297 (1959)Google Scholar
  4. 4.
    P. Erdös and A. Rényi: On the strength of connectedness of a random graph. Acta Mathematica, Vol. 12, pp. 261–267 (1961)Google Scholar
  5. 5.
    H. Frank and I. T. Frisch: Communication, Transmission, and Transportation Networks. Addison-Wesley, Reading, Massachusetts (1971)Google Scholar
  6. 6.
    H. Imai: On the practical efficiency of various maximum flow algorithms. Journal of the Operations Research Society of Japan, Vol. 26, pp. 61–83 (1983)Google Scholar
  7. 7.
    H. Imai and M. Iri: Practical efficiencies of existing shortest-path algorithms and a new bucket algorithm. Journal of the Operations Research Society of Japan, Vol. 27, pp. 43–58 (1984)Google Scholar
  8. 8.
    M. Iri, K. Murota and S. Matsui: An approximate solution for the problem of optimizing the plotter pen movement. In: R. F. Drenick and F. Kozin (ed.): System Modeling and Optimization (Proceedings of the 10th IFIP Conference on System Modeling and Optimization, New York, 1981), Lecture Notes in Control and Information Science 38, Springer-Verlag, Berlin, pp. 572–580 (1982)Google Scholar
  9. 9.
    T. Ohya, M. Iri and K. Murota: Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms. Journal of the Operations Research Society of Japan, Vol. 27, pp. 306–337 (1984)Google Scholar
  10. 10.
    V. Pan: How to Multiply Matrices Fast. Lecture Notes in Computer Science 179, Springer-Verlag, Berlin (1984)Google Scholar
  11. 11.
    K. Sugihara and M. Iri: Construction of the Voronoi diagram for “one million” generators in single-precision arithmetic. To appear in: G. T. Toussaint (ed.): Proceedings of IEEE — Special Issue on Computational Geometry (1992)Google Scholar
  12. 12.
    A. Taguchi and M. Iri: Continuum approximation to dense networks and its application to the analysis of urban networks. Mathematical Programming Study, Vol. 20, pp. 178–217 (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Masao Iri
    • 1
  1. 1.Department of Mathematical Engineering and Information Physics Faculty of EngineeringUniversity of TokyoTokyoJapan

Personalised recommendations