The densest k subgraph problem aims to find a subgraph $H$ of a graph $G$ with exactly $k$ vertices that maximizes the number of edges $|E(H)|$.
Does anyone know if there exists a polynomial-time algorithm for this problem under the restriction that $G$ is outerplanar? (Note: I am specifically asking for an algorithm, not a PTAS, and I want $G$ to be outerplanar, not $b$-outerplanar for some $b > 1$).