In this paper we show how parallel algorithms can be turned into efficient streaming algorithms for several classical combinatorial problems in the W − Stream . In this model, at each pass one input stream is read and one output stream is written; streams are pipelined in such a way that the output stream produced at pass i is given as input stream at pass i + 1. Our techniques give new insights on developing streaming algorithms and yield optimal algorithms (up to polylog factors) for several classical problems in this model including sorting, connectivity, minimum spanning tree, biconnected components, and maximal independent set.