Hi -- as many of you noticed, the last part of Problem 4 does not look so doable :)

The result is in fact true -- indeed, $\Omega(\log n)$ hardness for Set-Cover is known even subject to P $\neq$ NP. However the method illustrated probably won't cut it.

Please do one of the following instead:

1. Use this method to prove $f(n)$-hardness for Set-Cover, for as large a function $f(n)$ as you can -- subject to NP not in DTIME($2^{o(n)}$) or an even better DTIME assumption.

OR

2. Prove $\Omega(\log n)$-hardness for Set-Cover assuming NP not in BPTIME($n^{polylog n}$) -- using any method.

## Tuesday, February 26, 2008

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