Before revision:  In light of the lower bound we}{\pi}}\right) provide algorithms for estimating \alpha for arbitrary-length intervals under a bounded intersection assumption . We also study the parameterized space complexity of estimating \alpha and \beta, where the parameter is the ratio of maximum to minimum interval length .
After revision:  In light of the lower bound we}{\pi}}\right) provide algorithms for estimating \alpha for arbitrary-length intervals under a bounded intersection assumption and study the parameterized space complexity of estimating \alpha and \beta, where the parameter is the ratio of maximum to minimum interval length .