We present novel scalable parallel algorithms for finding global minimum cuts and connected components, which are important and fundamental problems in graph processing. To take advantage of future massively parallel architectures, our algorithms are
communication-avoiding
: they reduce the costs of communication across the network and the cache hierarchy. The fundamental technique underlying our work is the
randomized sparsification
of a graph: removing a fraction of graph edges, deriving a solution for such a sparsified graph, and using the result to obtain a solution for the original input. We design and implement sparsification with
O
(1) synchronization steps. Our global minimum cut algorithm decreases communication costs and computation compared to the state-of-the-art, while our connected components algorithm incurs few cache misses and synchronization steps. We validate our approach by evaluating MPI implementations of the algorithms on a petascale supercomputer. We also provide an approximate variant of the minimum cut algorithm and show that it approximates the exact solutions well while using a fraction of cores in a fraction of time.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.