  We study a generalization of the standard approval-based model of
participatory budgeting (PB), in which voters are providing approval ballots
over a set of predefined projects and -- in addition to a global budget limit,
there are several groupings of the projects, each group with its own budget
limit. We study the computational complexity of identifying project bundles
that maximize voter satisfaction while respecting all budget limits. We show
that the problem is generally intractable and describe efficient exact
algorithms for several special cases, including instances with only few groups
and instances where the group structure is close to be hierarchical, as well as
efficient approximation algorithms. Our results could allow, e.g.,
municipalities to hold richer PB processes that are thematically and
geographically inclusive.
