Bipartite Graph Matchings in the Semi-streaming Model

We present an algorithm for finding a large matching in a bipartite graph in the semi-streaming model. In this model, the input graph G = (V, E) is represented as a stream of its edges in some arbitrary order, and storage of the algorithm is bounded by O(n , polylog n) bits, where n = |V|. For e> 0, our algorithm finds a \(\frac{1}{1+\epsilon}\)-approximation of a maximum-cardinality matching and uses \(O{({(\frac{1}{\epsilon})^8})}\) passes over the input stream. The only previously known algorithm with such arbitrarily good approximation – though for general graphs – required exponentially many \(\Omega({{(\frac{1}{\epsilon})^{\frac{1}{\epsilon}}}})\) passes (McGregor 2005).