Assume having a graph $G_{variables}=(V,U)$ where $V=\{v_1,v_2,…,v_n\}$ is a set of variables; each variable $v_i\in V$ is associated with a set of possible values (it's domain) $dom(v_i)$.
Let $P$ be a search problem (i.e reachability problem) over graph $G=(O,E)$ where $O$ is the cartesian product of the variables domains. Let $T$ be a junction tree resulted from $G_{variables}$. $P$ can be also solved through searching every clique in $T$. I am looking for keywords/examples of such problems. $G_{variables}$ preferably to be DAG.