  The construction of specific supersymmetric grand unified models based on the
Pati-Salam gauge group and leading to a set of Yukawa quasi-unification
conditions which can allow an acceptable b-quark mass within the constrained
minimal supersymmetric standard model with mu>0 is briefly reviewed. Imposing
constraints from the cold dark matter abundance in the universe, B physics, and
the mass mh of the lighter neutral CP-even Higgs boson, we find that there is
an allowed parameter space with, approximately, 44<tanbeta<52,
-3<A0/M_{1/2}<0.1, 122<mh/GeV<127, and mass of the lightest sparticle in the
range (0.75-1.43) TeV. Such heavy lightest sparticle masses can become
consistent with the cold dark matter requirements on the lightest sparticle
relic density thanks to neutralino-stau coannihilations which are enhanced due
to stau-antistau coannihilation to down type fermions via a direct-channel
exchange of the heavier neutral CP-even Higgs boson. Restrictions on the model
parameters by the muon anomalous magnetic moment are also discussed.
