Why it matters

Set cover models many problems (scheduling, facility location). Understanding shapes approx.

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The architecture

Repeatedly pick largest set of uncovered.

Continue until universe covered.

Set cover greedyUncovered elementsremainingPick largest setgreedy choiceMark coveredrepeatAnalyzed via H_n = 1 + 1/2 + ... + 1/n; ln n approximation
Set cover.
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How it works end to end

Greedy: max marginal coverage.

Ln(n) bound proven.

Feige 1998: no better assuming P != NP.