In this work, a hierarchical search algorithm is proposed to efficiently compute the distance between similar tractography streamlines. This hierarchical framework offers an upper bound and a lower bound for the point-wise distance between two streamlines, which guarantees the validity of a proximity search. The proposed streamline representation enables the use of space-partitioning search trees to increase the tractography clustering speed without reducing its accuracy. The resulting approach enables a fast reconstruction a sparse distance matrix between two sets of streamlines, for all similar streamlines within a given radius. Alongside a white matter atlas, this fast streamline search can be used for accurate and reproducible tractogram clustering.