Back to the Coordinated Attack Problem

TL;DR

This paper analyzes the Coordinated Attack Problem under arbitrary omission faults, providing topological and combinatorial characterizations of message adversaries that prevent coordination, and presents algorithms illustrating these theoretical insights.

Contribution

It offers the first comprehensive topological and combinatorial characterization of message adversaries obstructing coordination without specific failure assumptions.

Findings

Characterizes message adversaries preventing coordination.

Provides two proofs: combinatorial and topological.

Introduces coordination algorithms based on these characterizations.

Abstract

We consider the well known Coordinated Attack Problem, where two generals have to decide on a common attack, when their messengers can be captured by the enemy. Informally, this problem represents the difficulties to agree in the presence of communication faults. We consider here only omission faults (loss of message), but contrary to previous studies, we do not to restrict the way messages can be lost, i.e. we make no specific assumption, we use no specific failure metric. In the large subclass of message adversaries where the double simultaneous omission can never happen, we characterize which ones are obstructions for the Coordinated Attack Problem. We give two proofs of this result. One is combinatorial and uses the classical bivalency technique for the necessary condition. The second is topological and uses simplicial complexes to prove the necessary condition. We also present two different Consensus algorithms that are combinatorial (resp. topological) in essence. Finally, we analyze the two proofs and illustrate the relationship between the combinatorial approach and the topological approach in the very general case of message adversaries. We show that the topological characterization gives a clearer explanation of why some message adversaries are obstructions or not. This result is a convincing illustration of the power of topological tools for distributed computability.