  This paper discusses a deterministic clustering approach to capacitated
resource allocation problems. In particular, the Deterministic Annealing (DA)
algorithm from the data-compression literature, which bears a distinct analogy
to the phase transformation under annealing process in statistical physics, is
adapted to address problems pertaining to clustering with several forms of size
constraints. These constraints are addressed through appropriate modifications
of the basic DA formulation by judiciously adjusting the free-energy function
in the DA algorithm. At a given value of the annealing parameter, the
iterations of the DA algorithm are of the form of a Descent Method, which
motivate scaling principles for faster convergence.
