General CONGEST Compilers against Adversarial Edges

We consider the adversarial CONGEST model of distributed computing in which a fixed number of edges (or nodes) in the graph are controlled by a computationally unbounded adversary that corrupts the computation by sending malicious messages over these (a-priori unknown) controlled edges. As in the standard CONGEST model, communication is synchronous, where per round each processor can send O ( log n ) bits to each of its neighbors. This paper is concerned with distributed algorithms that are both time efficient (in terms of the number of rounds), as well as, robust against a fixed number of adversarial edges. Unfortunately, the existing algorithms in this setting usually assume that the communication graph is complete ( n -clique), and very little is known for graphs with arbitrary topologies. We fill in this gap by extending the methodology of [Parter and Yogev, SODA 2019] and provide a compiler that simulates any CONGEST algorithm A (in the reliable setting) into an equivalent algorithm A ′ in the adversarial CONGEST model. Specifically, we show the following for every ( 2 f + 1 ) edge-connected graph of diameter D :