  A mixed dominating set $S$ of a graph $G=(V,E)$ is a subset $ S \subseteq V
\cup E$ such that each element $v\in (V \cup E) \setminus S$ is adjacent or
incident to at least one element in $S$. The mixed domination number
$\gamma_m(G)$ of a graph $G$ is the minimum cardinality among all mixed
dominating sets in $G$. The problem of finding $\gamma_{m}(G)$ is know to be
NP-complete. In this paper, we present an explicit polynomial-time algorithm to
construct a mixed dominating set of size $\gamma_{m}(G)$ by a parse tree when
$G$ is a generalized series-parallel graph.
