Skip to main content

Linear and book embeddings of graphs

  • Conference paper
  • First Online:
VLSI Algorithms and Architectures (AWOC 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 227))

Included in the following conference series:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F. Bernhart and B. Kainen, "The book thickness of a graph", J. Combinatorial Theory B, 27, 320–331, (1979).

    Google Scholar 

  2. J. F. Buss, and P. W. Shor, "On the pagenumber of planar graphs", Proc. 16th Ann. ACM Symp. on Theory of Computing, 98–100, (1984).

    Google Scholar 

  3. F. R. K. Chung, F. T. Leighton, and A. L. Rosenberg, "Diogenes: a methodology for designing fault-tolerant VLSI processor arrays", 13th Int'l Conf. on Fault-tolerant Computing, 26–32, (1983).

    Google Scholar 

  4. F. R. K. Chung, F. T. Leighton, and A.L. Rosenberg, "A graph layout problem with applications to VLSI design", (1984).

    Google Scholar 

  5. M. Chung, F. Makedon, I. H. Sudborough, J. Turner, "Polynomial time algorithms for the min cut problem on degree restricted trees". Proc. 23rd Annual Symp. on Foundations of Computer Science, 262–271, (1982).

    Google Scholar 

  6. D. Dolev and H. Trickey, "Embedding a tree on a line", IBM Technical Report, RJ3368, (1982).

    Google Scholar 

  7. S. Even, and A. Itai, "Queues, stacks and graphs", in Theory of Machines and Computations, Z. Kohavi and A. Paz, eds., Academic Press, NY, 71–86, (1971).

    Google Scholar 

  8. A. Feller, "Automatic layout of low-cost quick turnaround random-logic custom LSI devices", Proc. 13th Annual Design Automation Conference, 79–85, (1976).

    Google Scholar 

  9. M. J. Foster and H. T. Kung, "Recognizing regular languages with programmable building blocks", in VLSI-81, ed. J. P. Gray, Academic Press, 75–84, 1981.

    Google Scholar 

  10. R.A. Games, "Optimal book embeddings of the FFT, Benes, and barrel shifter networks", Third SIAM Conf. on Discrete Math., (1986).

    Google Scholar 

  11. F. Gavril, "Some NP-complete problems on graphs", Proc. 11th Conf. on Information Sciences and Systems, John Hopkins University, 91–95, (1977).

    Google Scholar 

  12. M. R. Garey, D. S. Johnson, G. L. Miller, and C. H. Papadimitriou, "The complexity of coloring circular arcs and chords", SIAM J. on Alg. and Disc. Meth., 1, 216–227, (1980).

    Google Scholar 

  13. M. C. Golumbic, Algorithmic graph theory and perfect graphs, Academic Press, 1980.

    Google Scholar 

  14. L. Heath, "Embedding planar graphs in seven pages", Proc. 25th Ann. Symp. on Foundations of Computer Science, 74–83, (1984).

    Google Scholar 

  15. L. Heath, "Algorithms for embedding graphs in books", Third SIAM Conf. on Discrete Math., (1986).

    Google Scholar 

  16. S. Istrail, "An algorithm for embedding planar graphs in six pages", private communication, (1985).

    Google Scholar 

  17. T. Lengauer, "Upper and lower bounds on the complexity of the min-cut linear arrangement problem on trees", SIAM J. Alg. Disc. Meth., (1982).

    Google Scholar 

  18. F. Makedon, I. H. Sudborough, "Minimizing width in linear layouts", Proc. 10th Intl. Coll. on Automata, Languages and Programming, 478–490, (1983).

    Google Scholar 

  19. F. Makedon, C. H. Papadimitriou, I. H. Sudborough, "Topological bandwidth", SIAM J. Alg. Disc. Meth., (1985).

    Google Scholar 

  20. G. Persky, D. Deutsch, D. Schweikert, "LTX-A minicomputer-based system for automated LSI layout", J. Design Automation and Fault Tolerant Computing,1, 217–255, (1977).

    Google Scholar 

  21. A. L. Rosenberg, "The Diogenes Approach to testable fault-tolerant arrays of processors", IEEE Trans. on Computing, C-32, 902–910, (1983).

    Google Scholar 

  22. P. Rosenstiehl, R. E. Tarjan, "Gauss codes, planar Hamiltonian graphs, and stack-sortable permutations", (1982).

    Google Scholar 

  23. R. E. Tarjan, "Sorting using networks of queues and stacks", J. Assoc. Comp. Mach., 19, 341–346, (1972).

    Google Scholar 

  24. A. Weinberger, "Large scale integration of MOS complex logic", IEEE J. Solid State Circuits, 182–190, (1967).

    Google Scholar 

  25. A. Wigderson, "The complexity of the Hamiltonian circuit problem for planar graphs", Princeton Univ. Tech. Report.

    Google Scholar 

  26. M. Yannakakis, "A polynomial algorithm for the min-cut linear arrangement of trees", J. ACM, 950–988, (1985).

    Google Scholar 

  27. M. Yannakakis, "Four pages are necessary and sufficient for planar graphs", Proc. 18th ACM Symp. on Theory of Computing, (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Filia Makedon Kurt Mehlhorn T. Papatheodorou P. Spirakis

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yannakakis, M. (1986). Linear and book embeddings of graphs. In: Makedon, F., Mehlhorn, K., Papatheodorou, T., Spirakis, P. (eds) VLSI Algorithms and Architectures. AWOC 1986. Lecture Notes in Computer Science, vol 227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16766-8_20

Download citation

  • DOI: https://doi.org/10.1007/3-540-16766-8_20

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16766-2

  • Online ISBN: 978-3-540-38746-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics