Solving the At-Most-Once Problem with Nearly Optimal Effectiveness

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 $m=O\left(\sqrt[3+\epsilon]{n/\log n}\right)$.
Comment: Updated Version. A Brief Announcement was published in PODC 2011. An Extended Abstract was published in the proceeding of ICDCN 2012. A full version was published in Theoretical Computer Science, Volume 496, 22 July 2013, Pages 69 - 88