Distributed scheduling for disconnected cooperation

Abstract

The dissertation studies how distributed devices that are disconnected for long and unknown periods can efficiently perform a set of tasks. Given n distributed devices that must perform t independent tasks, known to each device, the goal is to schedule work of the devices locally, in the absence of communication, so that when communication is established between some devices at some later point of time, the devices that connect have performed few tasks redundantly beyond necessity. The dissertation gives a lower bound on redundant work, and randomized and deterministic schedules, that allow devices to avoid doing redundant work provably well. The lower bound shows how the wasted work increases as the devices progress in their work. When each disconnected device randomly selects its next task, from among the tasks remaining to be done, then the amount of work duplicated by any devices that reconnect, is close to the lower bound in a precise sense. In order to derandomize the construction of schedules, techniques from design theory, linear algebra, and graph theory are used. The topics developed within the dissertation are related to the theory of latin squares and coding theory. For example the lower bound shown in the dissertation generalizes the Second Johnson Bound. The dissertation also studies scheduling problems for shared memory systems. It shows a method for creating near-optimal instances of an algorithm of Anderson and Woll. The dissertation also shows a work-optimal deterministic algorithm for the asynchronous Certified Write-All problem.