Abstract
In this paper, we consider the following problem of computational geometry which has direct applications to VLSI layout design : given a set of n isothetic solid rectangles on a rectangular floor, identify all maximal-empty-rectangles (MER's). A tighter upper bound on the number of MER's is derived. A new algorithm based on interval trees for identifying all MER's is then presented which runs in O(nlogn+R) time in the worst case and in O(nlogn) time in the average case, where R denotes the number of MER's. The space complexity of the algorithm is O(n). Finally, we explore the problem of recognizing the maximum (area)- empty- rectangle without explicitly generating all MER's. Our analysis shows that, on an average, around 70% of MER's need not be examined in order to locate the maximum. The proposed algorithm can readily be tailored to solve the MER problem in an ensemble of points as well as within an isothetic polygon.
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References
D. T. Lee and F. P. Preparata, “Computational geometry — a survey”, IEEE Trans. on Computers, Vol C-33, pp. 1072–1101, Dec. 1984.
A. Asano, M. Sato and T. Ohtsuki, “Computational geometry algorithms”, in Layout Design & Verification, Advances in CAD for VLSI, Vol-4, (Ed. T. Ohtsuki), pp. 295–347, North Holland, 1986.
T. G. Szymanski and C. J. Van Wyk, “Layout analysis and verification”, in Physical Design Automation of VLSI Systems, Ed. B. T. Preas and M. J. Lorenzette, Benjamin Cummings Publishing Company, Inc., 1988.
F. P. Preparata, and M. L. Shamos, Computational Geometry: An Introduction, Springer Verlag, NY, 1985.
Kurt Mehlhorn, Multidimensional Searching and Computational Geometry, Springer Verlag, NY, 1984.
D. Wood, “An isothetic view of computational geometry”, in Computational Geometry (G. T. Toussaint, Edited), North Holland, 1985.
J.L. Bentley and D. Wood, “An optimal worst case algorithm for reporting intersection of rectangles”, IEEE Trans. on Computers, Vol C-29, pp. 571–577, July 1980.
J.L. Bentley and T.A. Ottman, “Algorithms for reporting and counting geometric intersections”, IEEE Trans. on Computers, Vol C-28, pp. 643–647, Sept. 1979.
M. I. Shamos and D. Hoey, “Geometric intersection problems”, Proc. 17th Annual IEEE Symp. on Foundations of Computer Science, pp. 208–215, Oct. 1976.
K. Yoshida, “Layout verification”, in Layout Design and Verification, Ed. T. Ohtsuki, Elsevier Science Publication B.V.(North Holland), 1986.
A. Naamad, D. T. Lee and W. L. Hsu, “On the maximum empty rectangle problem”, Discrete Appl. Math.,8,1984, pp. 267–277.
S. Wimer and I. Koren, “Analysis of strategies for constructive general block placement”, IEEE Trans on CAD, Vol CAD-7, No. 3, pp. 371–377, 1988.
B. Chazelle, R.L. Drysdale and D.T. Lee, “Computing the largest empty rectangle “, SIAM J. Comput., Vol. 15, No. 1, pp. 300–315, February 1986.
M. J. Atallah and G. N. Frederickson, “A note on finding a maximum empty rectangle”, Discrete Applied Math., Vol. 13, pp. 87–91, 1986.
A. Aggarwal and S. Suri, “Fast algorithms for computing the largest empty rectangle”, Proc. 3rd Annual ACM Symp. on Computational Geometry, pp. 278–290, 1987.
M. Orlowski, “A new algorithm for the largest empty rectangle problem”, Algorithmica, Vol. 5, pp. 65–73, 1990.
T. Dey, “Two problems in computational geometry”, M.E. Thesis, Indian Institute of Science, Bangalore, India, 1987.
M.J. Atallah and S.R. Kosaraju, “An efficient algorithm for maxdominance, with applications”, Algorithmica, Vol. 4, pp. 221–236, 1989.
J.K. Ousterhout, “Corner stitching: data structuring technique for VLSI layout tools”,IEEE Trans. on CAD, Vol CAD-3No. 1, 1984, pp. 87–100.
D. E. Knuth, The Art of Computer Programming, Vol. 3, Sorting and Searching, Addison Wesley, 1973.
F. Harary, Graph Theory, Addison Wesley, 1972.
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Nandy, S.C., Bhattacharya, B.B., Ray, S. (1990). Efficient algorithms for identifying all maximal isothetic empty rectangles in VLSI layout design. In: Nori, K.V., Veni Madhavan, C.E. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1990. Lecture Notes in Computer Science, vol 472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53487-3_50
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DOI: https://doi.org/10.1007/3-540-53487-3_50
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