Abstract
This paper addresses a crucial question in VLSI floorplanning by rectangular dualization method: for any planar graph having a rectangular dual, does there exist a slicible dual? A minimum counterexample is presented and the concept of inherent nonslicibility is introduced. The problem of transforming a given nonslicible floorplan to a slicible one with change in shapes of a minimal subset of modules, is then formulated and a heuristic algorithm is proposed. The algorithm has a time complexity of O(n), where n is the number of modules in the floorplan.
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Bhasker, J. & S. Sahni, "A Linear Algorithm to find a Rectangular Dual of a Planar Triangulated Graph," Proc. 23rd Design Automation Conference, June 1986, pp. 108–114.
Bhasker, J. & S. Sahni, "A Linear Time Algorithm to Check for the Existence of a Rectangular Dual of a Planar Triangulated Graph," Networks, Vol. 17, 1987, pp. 307–317.
Dai, W.M. & E.S. Kuh, "Hierarchical Floor Planning for Building Block Layout," Proc. ICCAD, 1986, pp.454–457.
Harary, F., Graph Theory, Addison-Wesley Publishing Co., Reading, 1969.
Heller, W. R., G. Sorkin & K. Maling, "The Planar Package Planner for System Designers," Proc. 19th Design Automation Conference, 1982, pp.253–260.
Hu, T.C., & E.S. Kuh, "Theory and Concepts of Circuit Layout," Theory and Design of VLSI Layout, IEEE Press, 1986, pp. 3–18.
Garey, M. R. & D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, W.H. Freeman & Co., 1979.
Kozminski, K. & E. Kinnen, "An Algorithm for Finding a Rectangular Dual of a Planar Graph for Use in Area Planning for VLSI Integrated Circuits," Proc. 21st Design Automation Conference, June 1984, pp. 655–656.
Kozminski, K. & E. Kinnen, "Rectangular Dual of Planar Graphs," Networks, Vol. 15, No. 2, 1985, pp. 145–157.
LaPaugh, A.S., "Algorithms for Integrated Circuit Layout: An Analytic Approach," Ph.D. Thesis, M.I.T., 1980.
Leinwand, S. M., & Y.T. Lai, "An Algorithm for building Rectangular Floor-plans," Proc. 21st Design Automation Conference, 1984, pp. 663–664.
Luk, W. K., P. Sipala & C.K. Wong, "Minimum-area Wiring for Slicing Structures," IEEE Trans. on Computers, Vol. C-36, No.6, June 1987, pp. 745–760.
Otten, R.H.J.M., "Automatic Floorplan Design," Proc. 19th Design Automation Conference, 1982, pp. 261–267.
Otten, R.H.J.M., "Layout Structures," Proc. Large Scale Systems Symp. (IEEE), 1982, pp. 349–353.
Otten, R.H.J.M., "Efficient Floorplan Optimization," Proc. ICCD, 1983, pp. 499–502.
Ousterhout, J., G. Hamachi, R. Mayo, W.Scott & G. Taylor, "The MAGIC VLSI Layout System," IEEE Design and Test, Feb. 1985.
Rivest, R.L., "The PI (Placement and Interconnect) System," Proc. 19th Design Automation Conference, June 1982, pp. 475–481.
Stockmeyer, L.J., "Optimal Orientations of Cells in Slicing Floorplan designs," Information and Control, Vol. 57, 1983, pp. 91–101.
Supowit, K.J. & E.F. Slutz, "Placement Algorithms for Custom VLSI," Proc. 20th Design Automation Conference, June 1983, pp. 164–170.
Tsukiyama, S., K. Koike & I. Shirakawa, "An Algorithm to eliminate All Complex Triangles in a Maximal Planar Graph for use in VLSI Floor-plan," Proc. Intl. Symposium on Circuits and Systems (IEEE), 1986, pp.321–324.
Wong, D.F. & C.L. Liu, "A New Algorithm for Floorplan Design," Proc. 23rd Design Automation Conference, June 1986, pp. 101–107.
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© 1988 Springer-Verlag Berlin Heidelberg
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Sur-Kolay, S., Bhattacharya, B.B. (1988). Inherent nonslicibility of rectangular duals in VLSI floorplanning. In: Nori, K.V., Kumar, S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1988. Lecture Notes in Computer Science, vol 338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50517-2_73
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DOI: https://doi.org/10.1007/3-540-50517-2_73
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