• Corpus ID: 237091733

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… 
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2 Citations

2 Citations

On Two-Pass Streaming Algorithms for Maximum Bipartite Matching

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

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.

References

SHOWING 1-10 OF 84 REFERENCES

Deterministic Algorithms for Maximum Matching on General Graphs in the Semi-Streaming Model

An improved deterministic algorithm for Maximum Cardinality Matching on general graphs in the Semi-Streaming Model, where a graph is presented as a sequence of edges, and an algorithm must access the edges in the given sequence.

On Two-Pass Streaming Algorithms for Maximum Bipartite Matching

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.

Bipartite Matching in the Semi-streaming Model

We present the first deterministic 1+ε approximation algorithm for finding a large matching in a bipartite graph in the semi-streaming model which requires only O((1/ε)5) passes over the input…

Graph streaming lower bounds for parameter estimation and property testing via a streaming XOR lemma

A new lower bound technique is developed that proves that for many problems of interest, including all the above, obtaining a (1+є)-approximation requires either nΩ( 1) space or Ω(1/є) passes, even on highly restricted families of graphs such as bounded-degree planar graphs.

Almost optimal super-constant-pass streaming lower bounds for reachability

It is proved that the definition and construction of set hiding graphs are given, such that deciding whether i ∈ S boils down to deciding if ti is reachable from si, for a specific pair of vertices in the graph.

Near-Quadratic Lower Bounds for Two-Pass Graph Streaming Algorithms

  • Sepehr AssadiR. Raz
  • Computer Science, Mathematics
    2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
  • 2020
It is proved that any two-pass graph streaming algorithm for the s-t reachability problem in n-vertex directed graphs requires near-quadratic space of $n^{2-o(1)}$ bits, which implies that a wide range of graph problems admit essentially no non-trivial streaming algorithm even when two passes over the input is allowed.

Finding Large Matchings in Semi-Streaming

This work develops a 0:583-approximation 2-pass streaming algorithm to find the maximum matching in bipartite graphs, using O(n) space and a 3-pass algorithm, which is the first 3- pass streaming algorithm that achieves an approximation factor better than 0:6.

Semi-Streaming Bipartite Matching in Fewer Passes and Optimal Space

These techniques are deterministic and use optimal, O(n), space, improving upon the space complexity of the previous state-of-the-art Õ( −1)-pass algorithm of [AG18].

Better bounds for matchings in the streaming model

Improved bounds for approximating maximum matchings in bipartite graphs in the streaming model are presented and it is shown that a simple fractional load balancing approach achieves approximation ratio.

A Simple Augmentation Method for Matchings with Applications to Streaming Algorithms

  • C. Konrad
  • Computer Science, Mathematics
    MFCS
  • 2018
This paper shows that if G is bipartite, then running the Greedy matching algorithm on a sampled subgraph of G produces enough additional edges that can be used to augment M such that the resulting matching is of size at least (2 −√ 2) with high probability.
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