  We present and analyze a wait-free deterministic algorithm for solving the
at-most-once problem: how m shared-memory fail-prone processes perform
asynchronously n jobs at most once. Our algorithmic strategy provides for the
first time nearly optimal effectiveness, which is a measure that expresses the
total number of jobs completed in the worst case. The effectiveness of our
algorithm equals n-2m+2. This is up to an additive factor of m close to the
known effectiveness upper bound n-m+1 over all possible algorithms and improves
on the previously best known deterministic solutions that have effectiveness
only n-log m o(n). We also present an iterative version of our algorithm that
for any $m = O\left(\sqrt[3+\epsilon]{n/\log n}\right)$ is both
effectiveness-optimal and work-optimal, for any constant $\epsilon > 0$. We
then employ this algorithm to provide a new algorithmic solution for the
Write-All problem which is work optimal for any
$m=O\left(\sqrt[3+\epsilon]{n/\log n}\right)$.
