  Bootstrap particle filter (BPF) is the corner stone of many popular
algorithms used for solving inference problems involving time series that are
observed through noisy measurements in a non-linear and non-Gaussian context.
The long term stability of BPF arises from particle interactions which in the
context of modern parallel computing systems typically means that particle
information needs to be communicated between processing elements, which makes
parallel implementation of BPF nontrivial.
  In this paper we show that it is possible to constrain the interactions in a
way which, under some assumptions, enables the reduction of the cost of
communicating the particle information while still preserving the consistency
and the long term stability of the BPF. Numerical experiments demonstrate that
although the imposed constraints introduce additional error, the proposed
method shows potential to be the method of choice in certain settings.
