# A logarithmic boolean time algorithm for parallel polynomial division

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## Abstract

A new algorithm is presented to improve by a factor of log m the estimates for both parallel and sequential time complexity of division with a remainder of two integer polynomials. Under the parallel model, this means Boolean logarithmic time, which is asymptotically optimum. The algorithm exploits the reduction of the problem to integer division; the polynomial remainder and quotient are recovered from integer remainder and quotient via binary segmentation.

## Key Words

Parallel computational complexity Boolean circuit complexity polynomial division triangular Toeplitz matrix inversion interpolation by binary segmentation## Preview

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© Springer-Verlag Berlin Heidelberg 1986