Given a set of real numbers, choose a subset to maximize the average subject to the average not exceeding a given threshold. Is it NP hard?

I think so, but I cannot come out with a proof. Thanks a lot!!


This is at least as hard as the Subset Sum problem, hence, yes it is NP-hard.

  • $\begingroup$ Any suggestions for a rigorous proof? Thanks much! $\endgroup$
    – Tomlin
    Jul 19 '18 at 1:12
  • $\begingroup$ Hint: for nonempty $S$, $\textrm{average}(S) \leq 0 \leftrightarrow \textrm{sum}(S)\leq 0$. $\endgroup$
    – Yonatan N
    Jul 19 '18 at 4:40
  • $\begingroup$ Can you give more hint please? I do not know how to handle the cardinality $|S|$. $\endgroup$
    – Tomlin
    Jul 20 '18 at 6:02

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