Before revision:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega ] \left( \frac{n^{1/c}{2^c}} space.
After revision:  For arbitrary-length intervals, we show any c-approximation to \alpha , and thus also \beta , requires \Omega CP15] \left( \frac{n^{1/c}{2^c}} space.