An estimator for matching size in low arboricity graphs with two applications

In this paper, we present a new degree-based estimator for the size of maximum matching in bounded arboricity graphs. When graph is by $$\alpha $$ , gives +2$$ factor approximation size. For planar graphs, show does better and returns 3.5 Using estimator, get results approximating graphs streaming distributed models computation. particular, vertex-arrival streams, randomized $$O\left( \frac{\sqrt{n}}{\varepsilon ^2}\log n\right) space algorithm on n vertices within $$(3.5+\varepsilon )$$ factor. Similarly, simultaneous protocol vertex-partition model using \frac{n^{2/3}}{\varepsilon communication from each player. comparison with previous works, paper not need to know input improves case