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Topic: [Graph algorithm] Does this problem have a name ?
Replies: 2   Last Post: Aug 3, 2011 4:39 PM

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Dan Hoey

Posts: 172
Registered: 12/6/04
Re: [Graph algorithm] Does this problem have a name ?
Posted: Aug 3, 2011 3:16 PM
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On 8/3/11 1:30 PM, candide wrote:
> Consider the following question relative to graph theory :
> Let G a bipartite graph. To make the problem more concrete suppose G is
> the disjoint union of two sets, say I and S. Suppose
> *) I represents Individuals with name 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
> *) S represents Skills with name a,b, c, d, e, f, g, h.
> So, each individual has _some_ skills, for instance,
> -- individual 1 has skills b, d, g, and h,
> -- individual 2 has skills a, f, and h,
> -- etc.
> [in the example, datas are randomly given].
> We aim to build a team composed of the _minimum_ number of individuals
> from I in such a way that _every_ skill in S will be represented in the
> team, that is for each skill s in S, there exists a member of the team
> having the skill s.
> Does this problem have a name ? Does an efficient algorithm for solving
> it is known ?

You can transform this from a graph problem to a set problem by
providing as input the list of all the skill sets. The set problem is
called MINIMUM COVER in Garey and Johnson. It is NP-complete even if
each individual has exactly three skills, and even if we only want to
know whether there is an exact cover (a cover in which no skill is


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