  We apply Lattice-Linear Predicate Detection Technique to derive parallel and
distributed algorithms for various variants of the stable matching problem.
These problems are: (a) the constrained stable marriage problem (b) the super
stable marriage problem in presence of ties, and (c) the strongly stable
marriage in presence of ties. All these problems are solved using the
Lattice-Linear Predicate (LLP) algorithm showing its generality. The
constrained stable marriage problem is a version of finding the stable marriage
in presence of lattice-linear constraints such as ``Peter's regret is less than
that of Paul.'' For the constrained stable marriage problem, we present a
distributed algorithm that takes $O(n^2)$ messages each of size $O(\log n)$
where $n$ is the number of men in the problem. Our algorithm is completely
asynchronous. Our algorithms for the stable marriage problem with ties are also
parallel with no synchronization.
