  We study the ground state of few bosons with repulsive dipole-dipole
interaction in a quasi-one-dimensional harmonic trap by means of the exact
diagonalization method. Up to three interaction regimes are found depending on
the strength of the dipolar interaction and the ratio of transverse to axial
oscillator lengths: a regime where the dipolar Bose gas resembles a system of
weakly delta-interacting bosons, a second regime where the bosons are
fermionized, and a third regime where the bosons form a Wigner crystal. In the
first two regimes, the dipole-dipole potential can be replaced by a delta
potential. In the crystalline state, the overlap between the localized wave
packets is strongly reduced and all the properties of the boson system equal
those of its fermionic counterpart. The transition from the Tonks-Girardeau gas
to the solidlike state is accompanied by a rapid increase of the interaction
energy and a considerable change of the momentum distribution, which we trace
back to the different short-range correlations in the two interaction regimes.
