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Automated Lattice Drawing

  • Conference paper
Concept Lattices (ICFCA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2961))

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Abstract

Lattice diagrams, known as Hasse diagrams, have played an ever increasing role in lattice theory and fields that use lattices as a tool. Initially regarded with suspicion, they now play an important role in both pure lattice theory and in data representation. Now that lattices can be created by software, it is important to have software that can automatically draw them.

This paper covers:

  • The role and history of the diagram.

  • What constitutes a good diagram.

  • Algorithms to produce good diagrams.

Recent work on software incorporating these algorithms into a drawing program will also be covered.

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References

  1. Adams, M.E.: Uniquely complemented lattices. Selected Papers of Dilworth, R.P., Bogart, K., Freese, R., Kung, J. (eds.) The Dilworth Theorems, pp. 79–84. Birkhäuser, Basel (1990)

    Google Scholar 

  2. Aeschlimann, A., Schmid, J.: Drawing orders using less ink. Order 9, 5–13 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  3. Birkhoff, G.: Lattice theory, rev. ed. Amer. Math. Soc. Colloquium Publications, Providence (1948) (rev. ed.)

    Google Scholar 

  4. Day, A., Herrmann, C., Wille, R.: On modular lattices with four generators. Algebra Universalis 2, 317–323 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  5. Day, A., Freese, R.: A characterization of identities implying congruence modularity. I. Canad. J. Math. 32, 1140–1167 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dean, R.A.: Completely free lattices generated by partially ordered sets. Trans. Amer. Math. Soc. 83, 238–249 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  7. Dedekind, R.: Uber die von drei Moduln erzeugte Dualgruppe. Math. Annalen 53, 371–403 (1900)

    Article  MATH  MathSciNet  Google Scholar 

  8. Dilworth, R.P.: The role of order in lattice theory, Ordered Sets. In: Rival, I. (ed.) Proc. of the Banff Symposium on Ordered Sets, D. Reidel, Dordrecht (1982)

    Google Scholar 

  9. Eades, P., Wormald, N.: Edge crossings in drawings of bipartite graphs. Algorithmica 11(4), 379–403 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. Freese, R., Ježek, J., Nation, J.B.: Free lattices. Mathematical Surveys and Monographs, vol. 42. Amer. Math. Soc., Providence (1995)

    MATH  Google Scholar 

  11. Ganter, B., Wille, R.: Formal Concept Analysis. Springer, Heidelberg (1999) ISBN 3-540-62771-5

    MATH  Google Scholar 

  12. Garey, M., Johnson, D.: Computers and intractability, a guide to the theory of NP-completeness. W. H. Freeman and Company, San Francisco (1979)

    MATH  Google Scholar 

  13. Garey, M.R., Johnson, D.S.: Crossing number is NP-complete. SIAM J. Algebraic Discrete Methods 4(3), 312–316 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  14. Garg, A., Tamassia, R.: Advances in graph drawing, Algorithms and Complexity. In: Second Italian Conference, CASC 1994, Rome, Italy, pp. 12–21. Springer, Berlin (1994)

    Google Scholar 

  15. Knuth, D.E.: The art of computer programming, 2nd edn. Searching and Sorting, Addison- Wesley Series in Computer Science and Information Processing, vol. 3. Addison- Wesley Publishing Co., Reading (1998)

    Google Scholar 

  16. McLaughlin, J.E.: Atomic lattices with unique comparable complements. Proc. Amer. Math. Soc. 7, 864–866 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ore, O.: On the foundations of abstract algebra. I. Ann. Math. 36, 406–437 (1935)

    Article  MathSciNet  Google Scholar 

  18. Reid, C.: The search for E. T. Bell: also known as John Taine. Math. Assoc. Amer., Washington (1993)

    Google Scholar 

  19. Rival, I.: The diagram, Graphs and order. NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci, vol. 147, pp. 103–133. Reidel, Dordrecht (1985)

    Google Scholar 

  20. Rival, I.: Reading, drawing, and order, Algebras and orders. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci, vol. 389, pp. 359–404. Kluwer Acad. Publ., Dordrecht (1991)

    Google Scholar 

  21. Rival, I., Sands, B.: Pictures in lattice theory. Algebraic and geometric combinatorics 65, 341–355 (1982)

    Article  MathSciNet  Google Scholar 

  22. Rival, I., Wille, R.: Lattices freely generated by partially ordered sets: which can be drawn? J. Reine Angew. Math. 310, 56–80 (1979)

    Article  MathSciNet  Google Scholar 

  23. Rolf, H.L.: The free lattice generated by a set of chains. Pacific J. Math. 8, 585–595 (1958)

    MATH  MathSciNet  Google Scholar 

  24. Skorsky, M.: Endliche Verbände—Diagramme und Eigenschaften, Ph.D. thesis, Technische Hochschule Darmstadt (1992)

    Google Scholar 

  25. Stephan, J.: Liniendiagramme von verbänden, Technische Hochschule Darmstadt, Darmstadt, Diplomarbeit (1987)

    Google Scholar 

  26. Wille, R.: Lattices in data analysis: how to draw them with a computer. In: Rival, I. (ed.) Algorithms and order, Univ. Ottawa, pp. 33–58 (1989)

    Google Scholar 

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© 2004 Springer-Verlag Berlin Heidelberg

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Freese, R. (2004). Automated Lattice Drawing. In: Eklund, P. (eds) Concept Lattices. ICFCA 2004. Lecture Notes in Computer Science(), vol 2961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24651-0_12

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  • DOI: https://doi.org/10.1007/978-3-540-24651-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21043-6

  • Online ISBN: 978-3-540-24651-0

  • eBook Packages: Springer Book Archive

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