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Re: [igraph] set cover

From: Tamás Nepusz
Subject: Re: [igraph] set cover
Date: Tue, 24 Sep 2013 21:12:24 +0200

> 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


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