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In this paper, we introduce algorithms for constructing broadcasting and multicasting trees. These algorithms are general because they may be used for tree cost functions that are of arbitrary form. Thus, essentially the same algorithmic procedures are used for different tree cost functions. We evaluate the effectiveness of the general algorithms by applying them to different cost functions that are often used to model wired and wireless networks. Besides providing a unifying framework for dealing with many present and future tree-construction applications, these algorithms typically outperform some existing algorithms that are specifically designed for energy-aware wireless networks. These general algorithms perform well at the expense of higher computational complexity. They are centralized algorithms, requiring the full network information for tree construction. Thus, we also present variations of these general algorithms to yield other algorithms that have lower complexity and distributed implementation.