  We study spin chains with boundaries that are dual to open strings suspended
between systems of giant gravitons and dual giant gravitons. The anomalous
dimensions computed in the gauge theory are in complete quantitative agreement
with energies computed in the dual string theory. The comparison makes use of a
description in terms of magnons, generalizing results for a single maximal
giant graviton. The symmetries of the problem determine the structure of the
magnon boundary reflection/scattering matrix up to a phase. We compute a
reflection/scattering matrix element at weak coupling and verify that it is
consistent with the answer determined by symmetry. We find the
reflection/scattering matrix does not satisfy the boundary Yang-Baxter equation
so that the boundary condition on the open spin chain spoils integrability. We
also explain the interpretation of the double coset ansatz in the magnon
language.
