Improved Generation of Minimal Addition Chains

Authors:
Hatem M. Bahig
Affiliations:
Department of Mathematics/Computer Science, Faculty of Science, Ain Shams University, Cairo, Egypt
Venue:
Computing
Year:
2006

Citing 0
Cited 3

Erratum: erratum to "Some properties of nonstar steps in addition chains and new cases where the Scholz conjecture is true" [J. algorithms 42 (2002) 304-316]

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Abstract

An addition chain for a natural number n is a sequence 1=a0a1a r=n of numbers such that for each 0i≤r, a i=a j+a k for some 0≤k≤ji. An improvement by a factor of 2 in the generation of all minimal (or one) addition chains is achieved by finding sufficient conditions for star steps, computing what we will call nonstar lower bound in a minimal addition and omitting the sorting step.