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In this paper, we present a new simple degree-based estimator for the size ofmaximum matching in bounded arboricity graphs. When the arboricity of the graphis bounded by $\alpha$, the estimator gives a $\alpha+2$ factor approximationof the matching size. For planar graphs, we show the estimator does better andreturns a $3.5$ approximation of the matching size.  Using this estimator, we get new results for approximating the matching sizeof planar graphs in the streaming and distributed models of computation. Inparticular, in the vertex-arrival streams, we get a randomized$O(\frac{\sqrt{n}}{\epsilon^2}\log n)$ space algorithm for approximating thematching size within $(3.5+\epsilon)$ factor in a planar graph on $n$ vertices.Similarly, we get a simultaneous protocol in the vertex-partition model forapproximating the matching size within $(3.5+\epsilon)$ factor using$O(\frac{n^{2/3}}{\epsilon^2}\log n)$ communication from each player.  In comparison with the previous estimators, the estimator in this paper doesnot need to know the arboricity of the input graph and improves theapproximation factor for the case of planar graphs.

An Estimator for Matching Size in Low Arboricity Graphs with Two Applications