AbstractÐIntegrated Network Barriers (INBs) are a network protocol for parallel processors. INBs are both pipelinable and have low latency. In this paper, we show that INBs implement barriersÐwhich ensure that all prebarrier operations of any processor appear to complete before any post-barrier operationsÐand we show how to construct efficient, deadlock-free barriers for any interconnection network and routing function which has an acyclic queue dependency graph. As a special case, INBs can be implemented for any network and routing function for which there exists an acyclic channel dependency graph.