  We study the superfluid-insulator transition in a one dimensional system of
interacting bosons, modeled as a disordered Josephson array, using a strong
randomness real space renormalization group technique. Unlike perturbative
methods, this approach does not suffer from run-away flows and allows us to
study the complete phase diagram. We show that the superfluid insulator
transition is always Kosterlitz- Thouless like in the way that length and time
scales diverge at the critical point. Interestingly however, we find that the
transition at strong disorder occurs at a non universal value of the Luttinger
parameter, which depends on the disorder strength. This result places the
transition in a universality class different from the weak disorder transition
first analyzed by Giamarchi and Schulz [Europhys. Lett. {\bf 3}, 1287 (1987)].
While the details of the disorder potential are unimportant at the critical
point, the type of disorder does influence the properties of the insulating
phases. We find three classes of insulators which arise for different classes
of disorder potential. For disorder only in the charging energies and Josephson
coupling constants, at integer filling we find an incompressible but gapless
Mott glass phase. If both integer and half integer filling factors are allowed
then the corresponding phase is a random singlet insulator, which has a
divergent compressibility. Finally in a generic disorder potential the
insulator is a Bose glass with a finite compressibility.
