  Using a strong disorder real-space renormalization group (RG), we study the
phase diagram of a fully disordered chain of interacting bosons. Since this
approach does not suffer from run-away flows, it allows a direct study of the
insulating phases, which are not accessible in a weak disorder perturbative
treatment. We find that the universal properties of the insulating phase are
determined by the details and symmetries of the onsite chemical-potential
disorder. Three insulating phases are possible: (i) an incompressible Mott
glass with a finite superfluid susceptibility, (ii) a random-singlet glass with
diverging compressibility and superfluid susceptibility, (iii) a Bose glass
with a finite compressibility but diverging superfluid susceptibility. In
addition to characterizing the insulating phases, we show that the
superfluid-insulator transition is always of the Kosterlitz-Thouless
universality class.
