# Communication complexity of approximate maximum matching in the message-passing model

arXiv: https://arxiv.org/abs/1704.08462 · HTML: https://mlsanity.com/paper/1704.08462/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2017.

## Built on by (most cited first, 1 of 1)

- [Field Codes for Distributed Coupling Samplers and Certified Empirical Transport](https://mlsanity.com/paper/2607.27078/) (2026)

## Abstract (arXiv)

We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems, with a variety of applications. The input to the problem is a graph G that has n vertices and the set of edges partitioned over k sites, and an approximation ratio parameter α. The output is required to be a matching in G that has to be reported by one of the sites, whose size is at least factor α of the size of a maximum matching in G. We show that the communication complexity of this problem is Omega(α2 k n) information bits. This bound is shown to be tight up to a log n factor, by constructing an algorithm, establishing its correctness, and an upper bound on the communication cost. The lower bound also applies to other graph combinatorial problems in the message-passing communication model, including max-flow and graph sparsification.