  This paper brings explicit considerations of distributed computing
architectures and data structures into the rigorous design of Sequential Monte
Carlo (SMC) methods. A theoretical result established recently by the authors
shows that adapting interaction between particles to suitably control the
Effective Sample Size (ESS) is sufficient to guarantee stability of SMC
algorithms. Our objective is to leverage this result and devise algorithms
which are thus guaranteed to work well in a distributed setting. We make three
main contributions to achieve this. Firstly, we study mathematical properties
of the ESS as a function of matrices and graphs that parameterize the
interaction amongst particles. Secondly, we show how these graphs can be
induced by tree data structures which model the logical network topology of an
abstract distributed computing environment. Thirdly, we present efficient
distributed algorithms that achieve the desired ESS control, perform resampling
and operate on forests associated with these trees.
