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Maximum average weight ideal problems in ordered sets arise from modeling variants of the investment problem and, in particular, learning problems in the context of concepts with tree-structured attributes in artificial intelligence. Similarly, trying to construct tests with high reliability leads to a nontrivial maximum average weight ideal problem. This paper investigates the computational complexity and shows that the general problem is NP-complete. Important special cases (e.g., finding rooted subtrees of maximal average weight), however, can be handled with efficient algorithms.
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Faigle et al. (1994) studied this question.
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