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Gate matrix layout revisited: Algorithmic performance and probabilistic analysis

  • Geometric Algorithms
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 405))

Abstract

We consider the gate matrix layout problem for VLSI design, and improve the time and space complexities of an existing dynamic programming algorithm for its exact solution. Experimental study indicates the requirement of enormous computation time for exact solutions of even small size matrices. We derive an expression for the expected number of tracks required to layout in gate matrix style based on a probabilistic model. A local search approximation algorithm is studied experimentally and found to perform reasonably well on average.

This work was supported by grants from University of North Texas and U.S. Naval Training Systems Center.

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References

  1. Booth, K. S. and G. S. Leuker, “Testing for the Consecutive Ones Property, Interval Graphs and Graph Planarity Using PQ-Tree Algorithms,” J. Comput. Syst. Sci., Vol. 13, pp. 335–79, 1976.

    Google Scholar 

  2. Deo, N., M. S. Krishnamoorthy, and M. A. Langston, “Exact and Approximate Solutions for the Gate Matrix Layout Problem,” IEEE Trans. Computer-Aided Design, Vol. CAD-6, No. 1, pp. 79–84, Jan. 1987.

    Article  Google Scholar 

  3. Garey, M. R. and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Co., San Francisco, California, 1979.

    Google Scholar 

  4. Golumbic, M. C., Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1976.

    Google Scholar 

  5. Horowitz, E. and S. Sahni, Fundamentals of Computer Algorithms, Computer Science Press, Rockville, Maryland, 1978.

    Google Scholar 

  6. Kashiwabara, T. and T. Fujisawa, “An NP-Complete Problem on Interval Graph,” Proc. IEEE Int. Symp. Circuits and Systems, pp. 82–83, 1979.

    Google Scholar 

  7. Leong, H. W., “A New Algorithm for Gate Matrix Layout,” Proc. IEEE Int. Conf. Computer-Aided Design, Nov. 1986.

    Google Scholar 

  8. Li, J. T., “Algorithms for Gate Matrix Layout,” Proc. IEEE Int. Symp. Circuits and Systems, pp. 1013–16, 1983.

    Google Scholar 

  9. Lopez, A. D. and H. F. S. Law, “A Dense Gate Matrix Layout Method for MOS VLSI,” IEEE Trans. Electron Devices, pp. 1671–75, Aug. 1980.

    Google Scholar 

  10. Ohtsuki, T., H. Mori, E. S. Kuh, T. Kashiwabara, and T. Fujisawa, “One-Dimensional Logic Gate Assignment and Interval Graphs,” IEEE Trans. Circuits and Systems, Vol CAS-26, No. 9, pp. 675–84, Sept. 1979.

    Article  Google Scholar 

  11. Ohtsuki, T., H. Mori, T. Kashiwabara, and T. Fujisawa, “On Minimal Augmentation to a Graph to Obtain an Interval Graph,” J. Comput. Syst. Sci., pp. 60–97, Feb. 1981.

    Google Scholar 

  12. Prasad, S., Gate Matrix Layout: Expected-Case Analysis and Performance of Algorithms, M. S. Thesis, Dept. Comput. Sci., Washington State Univ., Pullman, WA, Aug. 1986.

    Google Scholar 

  13. Reingold, E. M., J. Nievergelt, and N. Deo, Combinatorial Algorithms: Theory and Practice, Prentice-Hall, Englewood Cliffs, New Jersey, 1977.

    Google Scholar 

  14. Wing, O., “Automated Gate Matrix Layout,” Proc. IEEE Int. Symp. Circuits and Systems, Rome, Italy, pp. 681–85, 1982.

    Google Scholar 

  15. Wing, O., “Interval-Graph-Based Circuit Layout,” Proc. IEEE Int. Conf. Computer-Aided Design, pp. 84–85, 1983.

    Google Scholar 

  16. Wing, O., S. Huang, and R. Wang, “Gate Matrix Layout,” IEEE Trans. Computer-Aided Design, Vol. CAD-4, No. 3, pp. 220–31, July 1985.

    Article  Google Scholar 

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C. E. Veni Madhavan

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© 1989 Springer-Verlag Berlin Heidelberg

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Das, S.K., Deo, N., Prasad, S. (1989). Gate matrix layout revisited: Algorithmic performance and probabilistic analysis. In: Veni Madhavan, C.E. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1989. Lecture Notes in Computer Science, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52048-1_50

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  • DOI: https://doi.org/10.1007/3-540-52048-1_50

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52048-1

  • Online ISBN: 978-3-540-46872-1

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