Parallel Dynamic Maximal Matching

Abstract

We present the first (randomized) parallel dynamic algorithm for maximal matching, which can process an arbitrary number of updates simultaneously. Given a batch of edge deletion or insertion updates to the graph, our parallel algorithm adjusts the maximal matching to these updates in poly(łog n) depth and using poly(łog n) amortized work per update. That is, the amortized work for processing a batch of k updates is k poly(łog n), while all this work is done in poly(łog n) depth, with high probability. This can be seen as a parallel counterpart of the sequential dynamic algorithms for constant-approximate and maximal matching [Onak and Rubinfeld STOC'10; Baswana, Gupta, and Sen FOCS'11; and Solomon FOCS'16]. Our algorithm readily generalizes to maximal matching in hypergraphs of rank r---where each hyperedge has at most r endpoints---with a poly(r) increase in work, while retaining the poly(łog n) depth.