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Re: [igraph] set cover

From: Raphael Clifford
Subject: Re: [igraph] set cover
Date: Tue, 24 Sep 2013 20:28:42 +0100

Thank you. I was looking for an exact (exponential time) solution.


On 24 September 2013 20:12, Tamás Nepusz <address@hidden> wrote:
>> I would like to solve an instance of minimum set cover. Is there some
>> way to do this by formulating it the problem as a bipartite graph and
>> using igraph?
> If you are looking for an exact solution, then the answer is probably no 
> (although I'm not 100% sure). However, there exists a greedy algorithm for 
> minimum set covers that achieves an approximation ratio of H(m) if there are 
> m items to be covered [1]. This greedy algorithm is fairly easy to implement:
> 1. Construct a bipartite graph where the first N vertices represent the sets 
> and the remaining M vertices represent the items to be covered. Connect an 
> item to a set if the item is in the set.
> 2. If there are no vertices to be covered, you are done.
> 3. Choose the set (i.e. the vertex among the first N vertices) with the 
> highest degree, add it to the cover and remove all its neighbors from the 
> graph.
> 4. Go to step 2.
> You can also combine the above technique with a local search using simulated 
> annealing or some other meta-heuristic, starting from the configuration given 
> by the greedy algorithm.
> [1] http://www.jstor.org/stable/3689577
> --
> T.
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