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Unformatted text preview: Greedy algorithm for Set cover Input: Collection C of sets S 1 ; :::; S m over a universe U . Weight w i for each set S i . Output: a subcollection C of smallest possible total weight whose union is also U . Whatever we need to minimize, can naturally be thought of as a cost. So we can think of w i as being the price of S i , and we want to buy all elements in U by buying some of the sets while minimizing what we spend. The natural greedy idea is: Pick the set that gives the maximum number of elements for the money that you spend on it. Setcover( C; U ) f 1. Mark all elements of U \uncovered". 2. C = null. 3. while some elements are uncovered: For each S j = 2 C compute the per element covering cost c j = w j /number of uncovered elements in S j . Pick the set S k that has minimum c k . Include S k in C . Mark the uncovered elements in S k covered. 4. Return C g The analysis is quite direct, we bound N i the number of elements remaining uncovered at the end of iteration i . We de ne N to mean...
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This note was uploaded on 01/04/2010 for the course CSE CS601 taught by Professor Prof.ranade during the Summer '09 term at IIT Bombay.
- Summer '09