A set S of vertices is a dominating set of G if every vertex not in S is adjacent to at least one member of S. An independent dominating set I of G is a dominating set of G if no two vertices of I are adjacent. The domination problem is NP-complete for an arbitrary graph. Here we focus on weighted trees. A weighted tree (T, w) is a tree together with a positive weight function on the vertex set w : V (T ) → R + . The weighted domination number γ w (T ) of (T, w) is the minimum weight w(D) = v∈D

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... w(v) of a dominating set D of T . The weighted independent domination number i w (T ) of (T, w) is the minimum weight w(I) = v∈I w(v) of an independent dominating set I of T . In this paper, we provide the liner-time algorithms for finding the weighted domination number and weighted independent domination number of a weighted tree. Mathematics Subject Classification: 05C69, 05C85