  In the Roman domination problem, an undirected simple graph $G(V,E)$ is
given. The objective of Roman domination problem is to find a function
$f:V\rightarrow {\{0,1,2\}}$ such that for any vertex $v\in V$ with $f(v)=0$
must be adjacent to at least one vertex $u\in V$ with $f(u)=2$ and $\sum_{u\in
V} f(u)$, called Roman domination number, is minimized. It is already proven
that the Roman domination problem (RDP) is NP-complete for general graphs and
it remains NP-complete for bipartite graphs. In this paper, we propose a
dynamic programming based polynomial time algorithm for RDP in convex bipartite
graph.
