Interconnection network with a shared whiteboard: Impact of (a)synchronicity on computing power

In this work we study the computational power of graph-based models of distributed computing in which each node additionally has access to a global whiteboard. A node can read the contents of the whiteboard and, when activated, can write one message of O(log n) bits on it. When the protocol terminates, each node computes the output based on the final contents of the whiteboard. We consider several scheduling schemes for nodes, providing a strict ordering of their power in terms of the problems which can be solved with exactly one activation per node. The problems used to separate the models are related to Maximal Independent Set, detection of cycles of length 4, and BFS spanning tree constructions.