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I/O Overhead and Parallel VLSI Architectures for Lattice Computations
July 1991 (vol. 40 no. 7)
pp. 843-852

The authors introduce input/output (I/O) overhead psi as a complexity measure for VLSI implementations of two-dimensional lattice computations of the type arising in the simulation of physical systems. It is shown by pebbling arguments that psi = Omega (n/sup -1/) when there are n/sup 2/ processing elements available. If the results must be observed at every generation and if no on-chip storage is allowed, the lower bound is the constant 2. The authors then examine four VLSI architectures and show that one of them, the multigeneration sweep architecture also has I/O overhead proportional to n/sup -1/. A closed-form for the discrete minimization equation giving the optimal number of generations to compute for the multigeneration sweep architecture is proved.

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Index Terms:
input/output overhead; parallel VLSI architectures; complexity measure; VLSI implementations; lattice computations; physical systems; multigeneration sweep architecture; computational complexity; lattice theory and statistics; parallel architectures; physics computing.
M.H. Nodine, D.P. Lopresti, J.S. Vitter, "I/O Overhead and Parallel VLSI Architectures for Lattice Computations," IEEE Transactions on Computers, vol. 40, no. 7, pp. 843-852, July 1991, doi:10.1109/12.83622
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