Randomized Work-Competitive Scheduling for Cooperative Computing on $k$-partite Task Graphs

A fundamental problem in distributed computing is the task of cooperatively executing a given set of $t$ tasks by $p$ processors where the communication medium is dynamic and subject to failures. The dynamics of the communication medium lead to groups of processors being disconnected and possibly reconnected during the entire course of the computation furthermore tasks can have dependencies among them. In this paper, we present a randomized algorithm whose competitive ratio is dependent on the dynamics of the communication medium and also on the nature of the dependencies among the tasks.