Question

Following is the input set given.

1009 2000
1009 2001
1002 2002
1003 2002 

Each line represents one group, Number represents ID of the member in the group. Problem is to choose minimum number of people which re-presents complete given set. Only one member should be choose from each Group. 2-tuple members will not repeated. But members can be part of more than one group.

So in this example answer be 1009 and 2002 which represents the sets. 1009 is chosen because it is representing two team and same is the case for 2002.

I am looking for what algorithm can be used to solve this problem.

Another example:

1009 2000
1009 2001
1002 2002
1003 2002 
1004 2003

Answer can be { 1009 , 2002, 1004} or { 1009, 2002, 2003}

Answer 1

Actually, the example given by Sodved shows, that I was wrong. It is not solved by the edge cover, as that still leaves the problem of selecting the actual vertices.