  An analysis of supersymmetric dark matter under the Yukawa unification
constraint is given. The analysis utilizes the recently discovered region of
the parameter space of models with gaugino mass nonuniversalities where large
negative supersymmetric corrections to the b quark mass appear to allow
$b-\tau$ unification for a positive $\mu$ sign consistent with the $b\to
s+\gamma$ and $g_{\mu}-2$ constraints. In the present analysis we use the
revised theoretical determination of $a_{\mu}^{SM}$ ($a_{\mu}= (g_{\mu}-2)/2$)
in computing the difference $a_{\mu}^{exp}-a_{\mu}^{SM}$ which takes account of
a reevaluation of the light by light contribution which has a positive sign.
The analysis shows that the region of the parameter space with
nonuniversalities of the gaugino masses which allows for unification of Yukawa
couplings also contains regions which allow satisfaction of the relic density
constraint. Specifically we find that the lightest neutralino mass consistent
with the relic density constraint, $b\tau$ unification for SU(5) and $b-t-\tau$
unification for SO(10) in addition to other constraints lies in the region
below 80 GeV. An analysis of the maximum and the minimum neutralino-proton
scalar cross section for the allowed parameter space including the effect of a
new determination of the pion-nucleon sigma term is also given. It is found
that the full parameter space for this class of models can be explored in the
next generation of proposed dark matter detectors.
