Approximate Maximum Matching in Random Streams
Abstract
In this paper, we study the problem of finding a maximum matching in the semistreaming model when edges arrive in a random order. In the semistreaming model, an algorithm receives a stream of edges and it is allowed to have a memory of $\tilde{O}(n)$ where $n$ is the number of vertices in the graph. A recent inspiring work by Assadi et al. shows that there exists a streaming algorithm with the approximation ratio of $\frac{2}{3}$ that uses $\tilde{O}(n^{1.5})$ memory. However, the memory of their algorithm is much larger than the memory constraint of the semistreaming algorithms. In this work, we further investigate this problem in the semistreaming model, and we present simple algorithms for approximating maximum matching in the semistreaming model. Our main results are as follows. We show that there exists a singlepass deterministic semistreaming algorithm that finds a $\frac{3}{5} (= 0.6)$ approximation of the maximum matching in bipartite graphs using $\tilde{O}(n)$ memory. This result significantly outperforms the stateoftheart result of Konrad that finds a $0.539$ approximation of the maximum matching using $\tilde{O}(n)$ memory. By giving a blackbox reduction from finding a matching in general graphs to finding a matching in bipartite graphs, we show there exists a singlepass deterministic semistreaming algorithm that finds a $\frac{6}{11} (\approx 0.545)$ approximation of the maximum matching in general graphs, improving upon the stateofart result $0.506$ approximation by Gamlath et al.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.10497
 Bibcode:
 2019arXiv191210497F
 Keywords:

 Computer Science  Data Structures and Algorithms