Distributed Algorithms for Matching in Hypergraphs

09/21/2020

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by   Oussama Hanguir, et al.

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We study the d-Uniform Hypergraph Matching (d-UHM) problem: given an n-vertex hypergraph G where every hyperedge is of size d, find a maximum cardinality set of disjoint hyperedges. For d≥3, the problem of finding the maximum matching is NP-complete, and was one of Karp's 21 𝒩𝒫-complete problems. In this paper we are interested in the problem of finding matchings in hypergraphs in the massively parallel computation (MPC) model that is a common abstraction of MapReduce-style computation. In this model, we present the first three parallel algorithms for d-Uniform Hypergraph Matching, and we analyse them in terms of resources such as memory usage, rounds of communication needed, and approximation ratio. The highlights include: ∙ A O(log n)-round d-approximation algorithm that uses O(nd) space per machine. ∙ A 3-round, O(d^2)-approximation algorithm that uses Õ(√(nm)) space per machine. ∙ A 3-round algorithm that computes a subgraph containing a (d-1+1/d)^2-approximation, using Õ(√(nm)) space per machine for linear hypergraphs, and Õ(n√(nm)) in general.