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Improved Generation of Minimal Addition Chains

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Abstract

An addition chain for a natural number n is a sequence 1=a 0<a 1< . . . <a r =n of numbers such that for each 0<i≤r, a i =a j +a k for some 0≤k≤j<i. 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.

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Authors and Affiliations

  1. Department of Mathematics/Computer Science, Faculty of Science, Ain Shams University, Cairo, Egypt

    Hatem M. Bahig

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  1. Hatem M. Bahig
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Correspondence to Hatem M. Bahig.

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Bahig, H.M. Improved Generation of Minimal Addition Chains. Computing 78, 161–172 (2006). https://doi.org/10.1007/s00607-006-0170-6

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  • DOI: https://doi.org/10.1007/s00607-006-0170-6

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