The complexity of greatest common divisor computations
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چکیده
We study the complexity of expressing the greatest common divisor of n positive numbers as a linear combination of the numbers. We prove the NP-completeness of finding an optimal set of multipliers with respect to either the L0 metric or the L∞ norm. We present and analyze a new method for expressing the gcd of n numbers as their linear combination and give an upper bound on the size of the largest multiplier produced by this method, which is optimal.
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تاریخ انتشار 1994