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Set-Covering Problem

Definition

Algorithm:

Greedy-Set-Cover(X, F)
$\;\;\;\;\;$U = X $\;\;\;\;\;$; uncovered
$\;\;\;\;\;$C = {}
$\;\;\;\;\;$while U $\neq$ {}
$\;\;\;\;\;$ $\;\;\;\;\;$select S $\in$ F maximizing \(\mid S \;\cap\; U \mid\)
$\;\;\;\;\;$ $\;\;\;\;\;$U = U - S
$\;\;\;\;\;$ $\;\;\;\;\;$C = C $\cup$ {S}
$\;\;\;\;\;$return C



Corollary 35.5

Greedy-Set-Cover has a ratio bound of (ln$\mid$X$\mid$ + 1).

Proof in book.


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