Greedy algorithm set cover

Question

In the below instance of set cover. How many sets the greedy algorithm will pick?. All sets have cost 1.

Can anyone explain me. What is the solution for this question.

So how will be greedy algorithm works for the 2nd instance.

how many sets it picks in the instance.

Please explain more what do you mean by set, and what criteria of picking and what do you mean by cost? — Abdennacer Lachiheb, Feb 08 '17 at 10:07
I found it on the mcq questions . The options for this question is a)2 , b) 3 , c) 4 , d)5. — Praveenkumar Beedanal, Feb 08 '17 at 10:13

score 2 · Accepted Answer · answered Feb 08 '17 at 10:22

2

Considering that greedy algorithm selects the best set each time if it this is determined by the number of points in each set it would first take the largest.

After it takes one it will remove the points which overlap from the remaining sets and again select the largest. So the remaining set would look like:

Therefore it should be 3 sets in the folding order:

This is a good problem which illustrates how it doesn't perform optimally because there is a possibility to solve the problem by taking only 2 sets. You can read a bit more here: http://pages.cs.wisc.edu/~shuchi/courses/787-F07/scribe-notes/lecture02.pdf

answered Feb 08 '17 at 10:22

Wald

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Thanks for your solution. – Praveenkumar Beedanal Feb 08 '17 at 10:38
can you please explain me the 2nd instance i edited now. – Praveenkumar Beedanal Feb 08 '17 at 11:14
What does the numbers around the sets mean ? Are they costs ? – Wald Feb 08 '17 at 16:08
@praveenkumarbeedanal it also depends based on what it determines the "better" set - cost, number of points in each set, etc. – Wald Feb 08 '17 at 16:37
@praveenkumarbeedanal well it depends on how it decides which is better if it is based on the cost and better = cheaper it will always take the cheapest so the pick order would be - > 1 1 2 3 and at that point it does have all the points and it would stop – Wald Feb 09 '17 at 07:51

Greedy algorithm set cover

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