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The following is a Maximum Bipartite matching problem : http://www.spoj.com/problems/QUEST4/ Through forums i came to know that the problem can be converted into a Minimum Vertex Cover problem, which in turn can be solved by Maximum Bipartite Matching. However, I do not understand how the problem has been converted into Minimum Vertex Cover. Please help me understand this.

rohitjv
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  • This question appears to be off-topic because it is not about programming. – user93353 Jul 27 '14 at 17:41
  • How is this not about programming? It is in general about algorithms. So, I think it is related to programming. Anyways, this question was asked long back, and the need is no longer required. – rohitjv Jul 28 '14 at 09:26
  • The rule is - if there is code in your question and the question is about the code, it belongs here - otherwise not - http://meta.stackexchange.com/questions/165519/where-should-i-post-questions-about-algorithms-stack-overflow-or-programmers-se – user93353 Jul 28 '14 at 09:44
  • OK. Thanks for the comment. I will take care while posting in the future. – rohitjv Jul 28 '14 at 11:55

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Let C , R be the set of all rows and all columns. Now let G be a bipartite graph having edges between C and R where there is an edge (i,j) from C to R if there is a hole in ith row and jth column.

Now consider the vertex cover of this graph. The vertex cover of a graph is a minimal set of nodes such that all edges are covered(each edge is incident upon at least one vertex in the vertex cover).

In our problem graph, each edge represents a hole. Vertices represent rows or columns. Objective- minimize blocks while covering all holes
which is equivalent to -
minimize vertices while covering all edges.

vikas
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