Massively Parallel Algorithms for Finding Well-Connected Components in Sparse Graphs
Sepehr Assadi, Xiaorui Sun, Omri Weinstein · 2019
Massively parallel computation (MPC) algorithms for graph problems have witnessed a resurgence of interest in recent years. Despite major progress for numerous graph problems however, the complexity of the sparse graph connectivity problem in this model has remained elusive: While classical logarithmic-round PRAM algorithms for finding connected components in any n-vertex graph have been known for more than three decades (and imply the same bounds for MPC model), no o(log n)-round MPC algorithms are known for this task with truly sublinear in n memory per machine (which is the only interesting regime for sparse graphs with O(n) edges). It is conjectured that an o(log n)-round algorithm for connectivity on general sparse graphs with n1-Ω (1) per-machine memory may not exist, a conjecture that also forms the basis for multiple conditional hardness results on the round complexity of other problems in the MPC model.