Set-Covering Problem

Definition

Algorithm:

• Greedy approach
• Grab the set covering the largest number of uncovered members

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

Corollary 37.5

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

Proof in book.