More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also be useful for analyzing distributed algorithms in failure-free networks of arbitrary structure. To illustrate this, we analyze consensus, set-agreement, and approximate agreement in networks, and derive lower bounds for these problems under classical computational settings, such as the LOCAL model and dynamic networks.
@article{arxiv.1907.03565,
title = {A Topological Perspective on Distributed Network Algorithms},
author = {Armando Castañeda and Pierre Fraigniaud and Ami Paz and Sergio Rajsbaum and Matthieu Roy and Corentin Travers},
journal= {arXiv preprint arXiv:1907.03565},
year = {2020}
}