  As two of the most important entanglement measures--the entanglement of
formation and the entanglement of distillation--have so far been limited to
bipartite settings, the study of other entanglement measures for multipartite
systems appears necessary. Here, connections between two other entanglement
measures--the relative entropy of entanglement and the geometric measure of
entanglement--are investigated. It is found that for arbitrary pure states the
latter gives rise to a lower bound on the former. For certain pure states, some
bipartite and some multipartite, this lower bound is saturated, and thus their
relative entropy of entanglement can be found analytically in terms of their
known geometric measure of entanglement. For certain mixed states, upper bounds
on the relative entropy of entanglement are also established. Numerical
evidence strongly suggests that these upper bounds are tight, i.e., they are
actually the relative entropy of entanglement.
