# Linear Programming in the Semi-streaming Model with Application to the Maximum Matching Problem

@inproceedings{Ahn2011LinearPI,
title={Linear Programming in the Semi-streaming Model with Application to the Maximum Matching Problem},
author={K. Ahn and Sudipto Guha},
booktitle={ICALP},
year={2011}
}
• Published in ICALP 12 April 2011
• Computer Science
In this paper, we study linear programming based approaches to the maximum matching problem in the semi-streaming model. The semi-streaming model has gained attention as a model for processing massive graphs as the importance of such graphs has increased. This is a model where edges are streamed-in in an adversarial order and we are allowed a space proportional to the number of vertices in a graph. In recent years, there has been several new results in this semistreaming model. However broad…

## Tables and Topics from this paper

Streaming Algorithms for Estimating the Matching Size in Planar Graphs and Beyond
• Computer Science, Mathematics
ACM Trans. Algorithms
• 2018
The adversarial-order model is circumvented by exploiting several structural properties of planar graphs, and more generally, graphs with bounded arboricity, and a reduction from the Boolean Hidden Matching Problem is designed to show that there is no randomized streaming algorithm that estimates the size of the maximum matching to within a factor better than 3/2 and uses only o(n1/2) bits of space.
Access to Data and Number of Iterations
• Computer Science
ACM Trans. Parallel Comput.
• 2018
This article provides an iterative sampling-based algorithm for computing a (1 − ε)-approximation of the weighted nonbipartite maximum matching that uses O(p/ε) rounds of sampling, and O(n1+1/p) space.
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.
Analyzing Massive Graphs in the Semi-streaming Model
A graph sparsification algorithm in the semi-streaming model, a sparse graph that approximately preserves all the cut values of a graph, and near-linear time algorithms for the $b$-matching problems which were not known before are presented.
Sublinear Estimation of Weighted Matchings in Dynamic Data Streams
• Computer Science, Mathematics
ESA
• 2015
An algorithm for estimating the weight of a maximum weighted matching by augmenting any estimation routine for the size of an unweighted matching is presented and the first constant estimation for the maximum matching size in a dynamic graph stream for planar graphs using $$\tilde{O}(n 4/5})$$ space is given.
Improved Bound for Matching in Random-Order Streams
This paper presents an algorithm that computes a 2/3(\sim.66)-approximate matching using only $O(n \log(n)$ space, improving upon both results above.
Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams
This paper presents a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams, and considers a larger family of parameterized problems for which this primitive yields fast, small-space dynamic graph stream algorithms.
Kernelization via Sampling with Applications to Dynamic Graph Streams
This paper presents a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams, and considers a larger family of parameterized problems for which this primitive yields fast, small-space dynamic graph stream algorithms.
Bipartite Matching in the Semi-streaming Model
• Mathematics, Computer Science
Algorithmica
• 2011
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
Approximating Semi-matchings in Streaming and in Two-Party Communication
• Mathematics, Computer Science
ACM Trans. Algorithms
• 2016
There is a hierarchical decomposition of an optimal semi-matching into maximum matchings and this result holds for semi- matchings that do not admit length-two degree-minimizing paths.

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