On Reachable Assignments Under Dichotomous Preferences

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