Advertisement

Reordering the Reorderable Matrix as an Algorithmic Problem

  • Erkki Mäkinen
  • Harri Siirtola
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1889)

Abstract

The Reorderable Matrix is a visualization method for tabular data. This paper deals with the algorithmic problems related to ordering the rows and columns in a Reorderable Matrix. We establish links between ordering the matrix and the well-known and much studied problem of drawing graphs. First, we show that, as in graph drawing, our problem allows different aesthetic criterions which reduce to known NP-complete problems. Second, we apply and compare two simple heuristics to the problem of reordering the Reorderable Matrix: a two-dimensional sort and a graph drawing algorithm.

Keywords

Bipartite Graph Black Area Algorithmic Problem Graph Drawing Bandwidth Minimization 
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.
    J. Bertin. Graphics and Graphic Information Processing. Walter de Gruyter & Co., Berlin, 1981. (Originally La graphique et le traitemente graphique de l’information, 1967, translated in English by William J. Berg and Paul Scott).Google Scholar
  2. 2.
    J. Bertin. Semiology of Graphics-Diagrams Networks Maps. The University of Wisconsin Press, 1983. (Originally Sémiologue graphique, 1967, translated in English by William J. Berg).Google Scholar
  3. 3.
    P. Z. Chinn, J. Chvátalová, A. K. Dewdney, and N. E. Gibbs, The bandwidth problem for graphs and matrices-a survey. J. Graph Theory 6 (1992), 223–254.CrossRefGoogle Scholar
  4. 4.
    G. Di Battista, P. Eades, R. Tamassia and I. G. Tollis, Annotated bibliography on graph drawing algorithms. Comput. Geom. Theory Appl. 4 (1994) 235–282.zbMATHGoogle Scholar
  5. 5.
    J. M. Dill, Optimal trie compaction is NP-complete. Cornell University, Dept. of Computer Science, Report 87-814, March 1987.Google Scholar
  6. 6.
    P. Eades and N. Wormald, Edge crossings in drawings of bipartite graphs. Algorithmica 10 (1994), 361–374.MathSciNetGoogle Scholar
  7. 7.
    M. R. Garey, R. L. Graham, D. S. Johnson, and D. E. Knuth, Complexity results for bandwidth minimization. SIAM J. Appl. Math. 34 (1978), 477–495.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness. W. H. Freeman, 1979.Google Scholar
  9. 9.
    H. Hinterberger and C. Schmid, Reducing the influence of biased graphical perception with automatic permutation matrices. In Proceedings of the Seventh Conference on Scientific Use of Statistic-Software, SoftStat93, Heidelberg. Gustav Fischer Verlag, Stuttgart, 1993, pages 285–291.Google Scholar
  10. 10.
    M. Jünger and P. Mutzel, 2-layer straightline crossing minimization: performance of exact and heuristic algorithms. J. Graph Algorithms and Applications 1 (1997), 1–25.MathSciNetGoogle Scholar
  11. 11.
    J. Katajainen and E. Mäkinen, A note on the complexity of trie compaction. EATCS Bull. 41 (1990), 212–216.zbMATHGoogle Scholar
  12. 12.
    D. J. Rose and R. E. Tarjan, Algorithmic aspects of vertex elimination of directed graphs. SIAM J. Appl. Math. 34 (1978), 176–197.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    H. Siirtola. Interaction with the Reorderable Matrix. In E. Banissi, F. Khosrowshahi, M. Sarfraz, E. Tatham, and A. Ursyn, editors, Information Visualization IV’99, pages 272–277. Proceedings International Conference on Information Visualization, IEEE Computer Society, July 1999. http://www.cs.uta.fi/~hs/iv99/siirtola.pdf.
  14. 14.
    K. Sugiyama, S. Tagawa, and M. Toda, Methods for visual understanding of hierarchical system structures. IEEE Trans. Syst. Man Cybern. SMC-11 (1981), 109–125.MathSciNetCrossRefGoogle Scholar
  15. 15.
    H. S. Wilf, On crossing numbers, and some unsolved problems. B. Bollobás and A. Thomason (eds), Combinatorics, Geometry, and Probability: A Tribute to Paul Erdös. Papers from the Conference in Honor of Erdös’ 80th Birthday Held at Trinity College, Cambridge University Press, 1997, pages 557–562.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Erkki Mäkinen
    • 1
  • Harri Siirtola
    • 1
  1. 1.Department of Computer and Information SciencesUniversity TampereFinland

Personalised recommendations