  In this paper we continue with the program to explore the topography of the
space of W-type algebras. In the present case, the starting point is the work
of Khesin, Lyubashenko and Roger on the algebra of q-deformed
pseudodifferential symbols and their associated integrable hierarchies. The
analysis goes on by studying the associated hamiltonian structures for which
compact expressions are found. The fundamental Poisson brackets yield
q-deformations of W_{KP} and related W-type algebras which, in specific cases,
coincide with the ones constructed by Frenkel and Reshetikhin. The construction
underlies a continuous correspondence between the hamiltonian structures of the
Toda lattice and the KP hierarchies.
