  We consider the problem of determining whether a target item assignment can
be reached from an initial item assignment by a sequence of pairwise exchanges
of items between agents. In particular, we consider the situation where each
agent has a dichotomous preference over the items, that is, each agent
evaluates each item as acceptable or unacceptable. Furthermore, we assume that
communication between agents is limited, and the relationship is represented by
an undirected graph. Then, a pair of agents can exchange their items only if
they are connected by an edge and the involved items are acceptable. We prove
that this problem is PSPACE-complete even when the communication graph is
complete (that is, every pair of agents can exchange their items), and this
problem can be solved in polynomial time if an input graph is a tree.
