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Heuristics and Experimental Design for Bigraph Crossing Number Minimization

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Algorithm Engineering and Experimentation (ALENEX 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1619))

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Abstract

The bigraph crossing problem, embedding the two vertex sets of a bipartite graph G = (V 0; V 1; E) along two parallel lines so that edge crossings are minimized, has application to circuit layout and graph drawing. We consider the case where both V 0 and V 1 can be permuted arbitrarily — both this and the case where the order of one vertex set is fixed are NP-hard. Two new heuristics that perform well on sparse graphs such as occur in circuit layout problems are presented. The new heuristics outperform existing heuristics on graph classes that range from application-specific to random. Our experimental design methodology ensures that differences in performance are statistically significant and not the result of minor variations in graph structure or input order.

This research has been supported by contracts from the Semiconductor Research Corporation (94-DJ-553), SEMATECH (94-DJ-800), DARPA/ARO (P-3316-EL/DAAH04-94-G-2080), and (DAAG55-97-1-0345), and a grant from Semiconductor Research Corporation.

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References

  1. F. Brglez, Design of Experiments to Evaluate CAD Algorithms: Which Improvements Are Due to Improved Heuristic and Which Are Merely Due to Chance?, Tech. Rep. 1998-TR@CBL-04-Brglez, CBL, CS Dept., NCSU, Box 7550, Raleigh, NC 27695, April 1998. Also available at http://www.cbl.ncsu.edu/publications/#1998-TR@CBL-04-Brglez.

  2. F. Brglez, N. Kapur, and D. Ghosh, A CBL PosterNote: Wire Crossing Problem and Benchmarking, aug 1997. Available from http://www.cbl.ncsu.edu/DiscussionGroups/Benchmark-reviews/frm00002.html.

  3. F. Brglez (Editor), A Brief Tour From The Home Page on WWW Statistical Experiment Archives: Benchmark Descriptions and Posted Solutions to NP-hard Problems, Tech. Rep. 1998-TR@CBL-01-Brglez, Version 1.0, CBL, CS Dept., NCSU, Box 7550, Raleigh, NC 27695, February 1998. Also available at http://www.cbl.ncsu.edu/publications/#1998-TR@CBL-01-Brglez.

  4. G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis, Graph Drawing: Algorithms for the Visualization of Graphs, Prentice Hall, 1999.

    Google Scholar 

  5. P. Eades and D. Kelly, Heuristics for reducing crossings in 2-layered networks, Ars Combinatoria, 21-A (1986), pp. 89–98.

    MathSciNet  Google Scholar 

  6. P. Eades, B. D. McKay, and N. C. Wormald, On an Edge Crossing Problem, tech. rep., Department of Computer Science, University of Newcastle, New South Wales 2308, Australia, 1976.

    Google Scholar 

  7. P. Eades and K. Sugiyama, How to Draw a Directed Graph, Journal of Information Processing, 13 (1990), pp. 424–437.

    MATH  Google Scholar 

  8. P. Eades and S. Whiteside, Drawing graphs in two layers, Theoretical Computer Science, 131 (1994), pp. 361–374.

    Article  MATH  MathSciNet  Google Scholar 

  9. P. Eades and N. C. Wormald, Edge Crossings in Drawings of Bipartite Graphs, Algorithmica, 11 (1994), pp. 379–403.

    Article  MATH  MathSciNet  Google Scholar 

  10. E.R. Gansner, E. Koutsifios, S.C. North and K.P. Vo, A Technique for Drawing Directed Graphs, IEEE Trans. Software Engg., 19 (1993), pp. 214–230. The drawing package dot is available from http://www.research.att.com/sw/tools/graphviz/.

    Article  Google Scholar 

  11. M. R. Garey and D. S. Johnson, Crossing Number is NP-complete, SIAM J. Algebraic Discrete Methods, 4 (1983), pp. 312–316.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Ghosh, F. Brglez, and M. Stallmann, First steps towards experimental design in evaluating layout algorithms: Wire length versus wire crossing in linear placement optimization, Tech. Rep. 1998-TR@CBL-11-Ghosh, CBL, CS Dept., NCSU, Box 7550, Raleigh, NC 27695, October 1998. Also available at http://www.cbl.ncsu.edu/publications/#1998-TR@CBL-11-Ghosh.

  13. —, Hypercrossing number: A new and effective cost function for cell placement optimization, Tech. Rep. 1998-TR@CBL-12-Ghosh, CBL, CS Dept., NCSU, Box 7550, Raleigh, NC 27695, December 1998. Also available at http://www.cbl.ncsu.edu/publications/#1998-TR@CBL-12-Ghosh.

  14. D. Ghosh, N. Kapur, J. E. Harlow, and F. Brglez, Synthesis of Wiring Signature-Invariant Equivalence Class Circuit Mutants and Applications to Benchmarking, in Proceedings, Design Automation and Test in Europe, Feb 1998, pp. 656–663. Also available at http://www.cbl.ncsu.edu/publications/#1998-DATE-Ghosh.

  15. F. Harary and A. J. Schwenk, Trees with Hamiltonian Square, Mathematika, 18 (1971), pp. 138–140.

    Article  MathSciNet  MATH  Google Scholar 

  16. —, A New Crossing Number for Bipartite Graphs, Utilitas Mathematica, 1 (1972), pp. 203–209.

    MATH  MathSciNet  Google Scholar 

  17. J. E. Harlow and F. Brglez, Design of Experiments in BDD Variable Ordering: Lessons Learned, in Proceedings of the International Conference on Computer Aided Design, ACM, Nov. 1998. Also available from http://www.cbl.ncsu.edu/publications/#1998-ICCAD-Harlow.

  18. M. JÜnger and P. Mutzel, 2-Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms, Journal of Graph Algorithms and Applications (JGAA), 1 (1997), pp. 1–25.

    Google Scholar 

  19. F. T. Leighton, New Lower Bound Techniques for VLSI, Math. Systems Theory, 17 (1984), pp. 47–70.

    Article  MATH  MathSciNet  Google Scholar 

  20. E. MÄkinen, A Note on the Median Heuristic for Drawing Bipartite Graphs, Fundamenta Informaticae, 12 (1989), pp. 563–570.

    MATH  MathSciNet  Google Scholar 

  21. —, Experiments on drawing 2-level hierarchical graphs, International Journal of Computer Mathematics, 37 (1990), pp. 129–135.

    Article  MATH  Google Scholar 

  22. M. Marek-Sadowska and M. Sarrafzadeh, The Crossing Distribution Problem, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 14 (1995), pp. 423–433.

    Article  Google Scholar 

  23. P. Mutzel, The AGD-Library: Algorithms for Graph Drawing, 1998. Available from http://www.mpi-sb.mpg.de/~mutzel/dfgdraw/agdlib.html.

  24. S. Yang, Logic Synthesis and Optimization Benchmarks User Guide, Tech. Rep. 1991-IWLS-UG-Saeyang, MCNC, Research Triangle Park, NC, January 1991. Now available from http://www.cbl.ncsu.edu/publications/#1991-IWLS-UG-Saeyang and benchmarks from http://www.cbl.ncsu.edu/benchmarks/Benchmarks-upto-1996.html.

  25. F. Shahrokhi, O. SÝkora, L. A. SZÉkely, and I. Vrt’o, On bipartite drawings and the linear arrangement problem, in Lecture Notes in Computer Science, no. 1467, Springer Verlag, 1997, pp. 55–68.

    Google Scholar 

  26. C. D. Thompson, Area-Time complexity for VLSI, in Proceedings, 11th Annual ACM Symposium on Theory of Computing, May 1979, pp. 81–88.

    Google Scholar 

  27. W. T. Tutte, Convex Representations of Graphs, Proc. London Math. Soc., 10 (1960), pp. 304–320.

    Article  MATH  MathSciNet  Google Scholar 

  28. —, How to Draw a Graph, Proc. London Math. Soc., 13 (1963), pp. 743–768.

    Article  MATH  MathSciNet  Google Scholar 

  29. J. N. Warfield, Crossing Theory and Hierarchy Mapping, IEEE Transactions on Systems, Man, and Cybernetics, SMC-7 (1977), pp. 505–523.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, N.C. State University, PO Box 8206, Raleigh, NC, 27695-8206, USA

    Matthias Stallmann, Franc Brglez & Debabrata Ghosh

Authors
  1. Matthias Stallmann
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  2. Franc Brglez
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  3. Debabrata Ghosh
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Editor information

Editors and Affiliations

  1. Department of Computer Science, John Hopkins University, Baltimore, MD, 21218, USA

    Michael T. Goodrich

  2. Department of Mathematics and Computer Science, Amherst University, Amherst, MA, 01002, USA

    Catherine C. McGeoch

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© 1999 Springer-Verlag Berlin Heidelberg

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Stallmann, M., Brglez, F., Ghosh, D. (1999). Heuristics and Experimental Design for Bigraph Crossing Number Minimization. In: Goodrich, M.T., McGeoch, C.C. (eds) Algorithm Engineering and Experimentation. ALENEX 1999. Lecture Notes in Computer Science, vol 1619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48518-X_5

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  • DOI: https://doi.org/10.1007/3-540-48518-X_5

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  • Print ISBN: 978-3-540-66227-3

  • Online ISBN: 978-3-540-48518-6

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