Maximum numbers of elements that can be eliminated from a set of sets?

[sebihp2007]

Hello

I have come across a problem lately. You are given a set of n sets with m variables.. for instance {a,b,c,d}, {b,c,d}, {b,c}, {c,e,f}, {e,f}. And you want to eliminate elements from these sets with the restriction that you can only eliminate one item from each set and each item can only be eliminated from one set (i.e. if you've eliminated b from set {a,b,c,d}, then you cannot eliminate it from {b,c,d}). The problem is writing an algorithm which determines the maximum number of elements you can eliminate. And I'm hopelessly stuck... of course, you could backtrack it and determine this number but I feel it could be done more efficiently.. it looks like something elementary which should be easy to figure out but I just can't get my head around it. Any help would be appreciated.

Thanks in advance :)

[ne555]

look for: "network flow --- bipartite matching"
there are two groups: elements and sets, an edge represents that the element is in that set.

[sebihp2007]

Thank you for this :).. it'll do for a good read.. it seems to be what I'm looking for