@article {IOPORT.05968764,
    author       = {Bahig, Hatem M.},
    title        = {Star reduction among minimal length addition chains.},
    year         = {2011},
    journal      = {Computing},
    volume       = {91},
    number       = {4},
    issn         = {0010-485X},
    pages        = {335-352},
    publisher    = {Springer-Verlag, Wien},
    doi          = {10.1007/s00607-010-0122-z},
    abstract     = {An addition chain for a natural number $n$ is a sequence $1=a_0 < a_1 < \cdots < a_r =n$ of integers such that for each $0 < i \le r$, $a_i = a_j+a_k$ for some $0\le k \le j <i$. The minimal length of an addition chain for $n$ is denoted by $\ell(n)$. If the above integer $j=i-1$, the step $i$ is called a {\it star step}. It is known that there is a minimal length addition chain for $n$ such that the last four steps are star steps. The author conjectures that this even true that there is a minimal length addition chain for $n$ such that the last $\lfloor \ell(n)/2 \rfloor$ steps are star steps and he verified that this holds for $n\le 2^{18}$. An application of this conjecture leads to significant progress for the cost of computing a minimal addition chain for $n$.},
    reviewer     = {Maurice Mignotte (Strasbourg)},
    identifier   = {05968764},
}