A robust randomized algorithm to perform independent tasks

The Do-All problem is about scheduling t similar and independent tasks to be performed by p processors prone to crashes. We assume that the distributed system is synchronous with processors communicating by message passing. Crashes are determined by a fully adaptive adversary that is restricted only by an upper bound f   on the number of crashes. The complexity of algorithms is measured by work and communication, where work is defined as the number of available-processor steps, and communication as the number of point-to-point messages. We develop a randomized algorithm with W=O(t+p⋅log2ploglogp) expected work and O((pp−f)3.4W) expected communication, for an arbitrary number f