Barriers due to Congestion and Two Ways to Deal With Them

Restricting the bandwidth in models of distributed graph computations naturally introduces challenges that arise due to communication bottlenecks. In this talk, I will survey techniques for proving lower bounds on the complexity of fundamental graph problems under limited bandwidth. For some problems, allowing relaxed solutions can significantly reduce the required amount of communication, enabling efficient computations. Two successful approaches for overcoming provable barriers, namely, approximations and testing, will be exemplified and discussed in the context of distributed computing.