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

TL;DR

This paper investigates how the use of a shared whiteboard in graph-based distributed computing models affects computational power under different scheduling schemes, focusing on problems like MIS, cycle detection, and BFS tree construction.

Contribution

It introduces a formal analysis of the impact of (a)synchronous scheduling on the computational capabilities of whiteboard-enabled distributed models.

Findings

Different scheduling schemes strictly affect problem-solving power.

Whiteboard access enables solving problems like MIS and cycle detection.

The models' power varies with the level of synchronicity.

Abstract

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.