09.05.2014 Views

Set cover problem: definition - Organic Origami

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Can we do better?<br />

Actually, NO!<br />

It has been shown that for any c > 0, if there is an approximation<br />

algorithm for set <strong>cover</strong> with guarantee at most (1 − c) ln n, then<br />

(well, not actually P=NP, but something just as unlikely: every<br />

<strong>problem</strong> in NP could then be solved in time O(n polylog(n) ), which is<br />

not thought to be possible. . . )

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