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A unified approach to layout wirability

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Abstract

We consider the problem of wiring planar knock-knee mode layouts. We present a systematic approach to this problem and develop a unified framework that also applies to layouts using grids that are more general than the usual square grid, and determine all possible grids that satisfy some natural regularity criteria. We develop some specific techniques for wiring of layouts in the square grid. As one of the applications of these techniques, we give a simple characterization of two-layer wirability of an arbitrary layout.

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References

  1. R. L. Rivest, A. Baratz, and G. Miller, Provably good channel routing algorithms, inVLSI Systems and Computations (H. T. Kung, B. Sproull, and G. Steele, eds), Computer Science Press, Rockville, MD, 1981, pp. 153–159.

    Google Scholar 

  2. T. Bolognesi and D. J. Brown, A channel routing algorithm with bounded maximum wire length, Manuscript, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1982.

  3. F. P. Preparata and W. Lipski, Three layers are enough,Proceedings of the 23rd Symposium on Foundations of Computer Science, Chicago, IL, November 3–5, 1982, pp. 350–357.

  4. F. P. Preparata and W. Lipski, Optimal three-layer channel routing,IEEE Trans. Comput.,33 (1984), 427–437.

    Google Scholar 

  5. W. Lipski, On the structure of three-layer wirable layouts, inAdvances in Computing Research: VLSI Theory, JAI Press, Greenwich, CT, 1984, pp. 231–243.

    Google Scholar 

  6. M. L. Brady and D. J. Brown, VLSI routing: four layers suffice, inAdvances in Computing Research: VLSI Theory, JAI Press, Greenwich, CT, 1984, pp. 245–257.

    Google Scholar 

  7. T. L. Saaty and P. C. Kainen,The Four-Color Problem, McGraw-Hill, New York, 1977.

    Google Scholar 

  8. B. Bollobàs,Graph Theory, Springer-Verlag, New York, 1979.

    Google Scholar 

  9. W. Lipski, E. Lodi, F. Luccio, C. Mugnai and L. Pagli, On two-dimensional data organization, II,Fund. Inform.,2 (1979), 245–260.

    Google Scholar 

  10. K. Mehlhorn and F. P. Preparata, Routing through a rectangle,J. Assoc. Comput. Mach.,33 (1985), 60–85.

    Google Scholar 

  11. L. Fejes Tóth,Regular Figures, Pergamon Press, Oxford, 1984.

    Google Scholar 

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On leave from the Institute of Computer Science, Polish Academy of Sciences, P.O. Box 22, 00-901 Warsaw, Poland. W. Lipski tragically died on May 30, 1985.

The work of F. P. Preparata was supported in part by the Semiconductor Research Corporation under Contract SRC RSCH 84-06-049.

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Lipski, W., Preparata, F.P. A unified approach to layout wirability. Math. Systems Theory 19, 189–203 (1986). https://doi.org/10.1007/BF01704913

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  • DOI: https://doi.org/10.1007/BF01704913

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