  Let $G=(V,E)$ be a graph. Let $w$ be a positive integer. A $w$-dominating set
is a vertex subset $S$ such that for all $v\in V$, either $v\in S$ or it has at
least $w$ neighbors in $S$. The $w$-Dominating Set problem is to find the
minimum $w$-dominating set. The $L$-Max $w$-Dominating Set problem is to find
the vertex subset $S$ of cardinality at most $L$ that maximizes $|S|+|\{v\in
V\setminus S~|~|N(v)\cap S|\geq w\}|$, where $N(v)=\{u|uv\in E\}$. In this
paper, we give polynomial time algorithms to $w$-Dominating Set problem and
$L$-Max $w$-Dominating Set problem on graphs of bounded treewidth.
