Before revision:  We give the first {\em single pass} sketching algorithm for constructing graph spanners: we show how to obtain a O(n^{ \frac{2 \frac23 })-spanner using O(n) space, and in general a O(n^{ \frac{2 \frac23 (1-\alpha)})-spanner using O(n^{1+\alpha}) space for every \alpha\in [0, 1], a tradeoff that we think may be close optimal.
After revision:  We give the first {\em single pass} sketching algorithm for constructing graph spanners: we show how to obtain a O(n^{ \frac23 })-spanner using O(n) space, and in general a O(n^{ \frac{2 \frac23 (1-\alpha)})-spanner using O(n^{1+\alpha}) space for every \alpha\in [0, 1], a tradeoff that we think may be close optimal.