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A Space-and-Time-Efficient Coding Algorithm for Lattice Computations
October 1994 (vol. 6 no. 5)
pp. 819-829

We present an encoding algorithm for lattices that significantly reduces space requirements while allowing fast computations of least upper bounds and greatest lower bounds of pairs of elements. We analyze the algorithms for encoding, LUB and GLB computations, and prove their correctness. Empirical experiments reveal that our method is significantly more space efficient than the transitive closure method, and the saving becomes increasingly more important as the size of the lattice increases.

[1] H. Aït Kaci, "An algebraic-semantic approach to the effective resolution of types equations,"Theor. Comput. Sci.vol. 45, pp. 185-215, 1986.
[2] H. Ait-Kaci, R. Boyer, P. Lincoln, and R. Nasr, "Efficient implementation of lattice operations,"ACM Trans. Program. Lang. Syst., vol. 11, no. 1, pp. 115-146, Jan. 1989.
[3] G. Birkhoff,Lattice Theory, 3rd ed. American Mathematical Society Colloquium Publications, vol. 25, 1979.
[4] M. A. Taalebinezhaad, "Partial implementation of fixation method on real images," inProc. IEEE Conf. Computer Vision Pattern Recognition(Maui, Hawaii), June 1991.
[5] J. P. Tremblay and R. Manohar,Discrete Mathematical Structures with Applications to Computer Science, New York: McGraw-Hill, 1987.

Index Terms:
encoding; inheritance; inference mechanisms; space-and-time-efficient coding algorithm; lattice computations; encoding algorithm; space requirements
Citation:
D.D. Ganguly, C.K. Mohan, S. Ranka, "A Space-and-Time-Efficient Coding Algorithm for Lattice Computations," IEEE Transactions on Knowledge and Data Engineering, vol. 6, no. 5, pp. 819-829, Oct. 1994, doi:10.1109/69.317709
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