This work bridges the gap between distributed and centralised models of computing in the context of sublinear-time graph algorithms. A priori, typical centralised models of computing (e.g., parallel decision trees or centralised local algorithms) seem to be much more powerful than distributed message-passing algorithms: centralised algorithms can directly probe any part of the input, while in distributed algorithms nodes can only communicate with their immediate neighbours. We show that for a large class of graph problems, this extra freedom does not help centralised algorithms at all: for example, efficient stateless deterministic centralised local algorithms can be simulated with efficient distributed message-passing algorithms. In particular, this enables us to transfer existing lower bound results from distributed algorithms to centralised local algorithms.
@article{arxiv.1512.05411,
title = {Non-Local Probes Do Not Help with Graph Problems},
author = {Mika Göös and Juho Hirvonen and Reut Levi and Moti Medina and Jukka Suomela},
journal= {arXiv preprint arXiv:1512.05411},
year = {2015}
}