Brief announcement: exponential speed-up of local algorithms using non-local communication

We demonstrate how to leverage a system's capability for all-to-all communication to achieve an exponential speed-up of local algorithms despite bandwidth and memory restrictions. More precisely, if a network comprises <i>n</i> nodes with all-to-all bandwidth <i>n</i>^ε (ε > 0 constant) and nodes know their input and neighborhood with respect to a graph problem instance of polylogarithmic maximum degree, any local algorithm for this problem with running time <i>r</i> ∈ <i>O</i>(log <i>n</i>) and reasonably small states can be simulated within <i>O</i>(log <i>r</i>) rounds.