# A Two-Pass Lower Bound for Semi-Streaming Maximum Matching

@article{Assadi2021ATL, title={A Two-Pass Lower Bound for Semi-Streaming Maximum Matching}, author={Sepehr Assadi}, journal={ArXiv}, year={2021}, volume={abs/2108.07187} }

We prove a lower bound on the space complexity of two-pass semi-streaming algorithms that approximate the maximum matching problem. The lower bound is parameterized by the density of Ruzsa-Szemerédi graphs : • Any two-pass semi-streaming algorithm for maximum matching has approximation ratio at least ( 1− Ω( log RS(n) logn ) ) , where RS(n) denotes the maximum number of induced matchings of size Θ(n) in any n-vertex graph, i.e., the largest density of a Ruzsa-Szemerédi graph. Currently, it is…

## 2 Citations

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By optimizing parameters, it is discovered that Konrad’s algorithm is optimal for the implied class of algorithms and, perhaps surprisingly, that there is a second optimal algorithm.

### CMSC 858M: Algorithmic Lower Bounds: Fun with Hardness Proofs

- Computer Science
- 2022

This chapter considers straming algorithms which are very similar to online algorithms, and builds reductions from the INDEX problem such that the partially seen input encodes the array X and the unseen part of the input determines the index i.

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