I want a hueristic algorithm for the following problem. Here, $V(G)$, $E(G)$ respectively refer to the vertex set and edge set of a graph $G$.
Input: two planar bipartite graphs, $G,H$ and a map $\phi: A\to V(H)$, where $A$ is a subset of $V(G)$.
Task: determine if there is a (bijective) map $\phi': V(G) \to V(H)$, such that $(\phi(x),\phi(y)) \in E(H) \iff (x,y) \in E(G)$, and the restriction $\phi'\mid_A$ is $\phi$. (i.e. $\phi'(a) = \phi(a)$ for all $a \in A$)
Does there exist a practical fast running algorithm for determining if such a $\phi'$ exists? If not, does there exist a simple heuristic algorithm which has a "decent chance" of answering in the affirmative.
I'm looking for an algorithm I can actually understand and code myself, rather than use a large complicated system like