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I have seen a question on 2-approximation algorithm for Vertex-Cover problem(VC, known Np-Complete problem), and i don't know the answer. The problem is the following : Find a 2-approximation algorithm for Vertex Cover problem using "Spanning Tree". Well, many greedy approaches are already presented for VC, but special algorithm using "Spanning Tree" is challenging. Any idea?

parsa rastegari
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  • There's a separate Stack Exchange for theoretical computer science (http://cstheory.stackexchange.com/) -- you might do better getting your question answered there. – Martin B Jan 31 '11 at 17:13
  • Oh, Thanks for your note. I did it now. – parsa rastegari Jan 31 '11 at 17:15
  • Yep, that's not research, i do study algorithms for a competition and sometimes i need help. Doesn't anybody know the answer? any idea? – parsa rastegari Jan 31 '11 at 17:58
  • @parsa: This question is probably off-topic for cstheory, which is a site for research level questions. Not homework level questions (looks like that to me from the way it is stated). Mostly likely it will be closed as off-topic, if it is really homework level. –  Jan 31 '11 at 17:58
  • Before it gets closed here too: The following paper is probably useful: https://bora.uib.no/bitstream/1956/1112/15/Paper%201.pdf –  Jan 31 '11 at 18:01
  • homework? tag it as homewomwork, this is a problem in vazirani book. – Saeed Amiri Feb 01 '11 at 18:05

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You just search for max matching in the given graph and the solution is the set of nodes that create a max matching.

ShaQ
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  • Can you elaborate on this? How do you get from a set of edges to a set of vertices? – templatetypedef Feb 01 '11 at 17:55
  • Ok so: Max Matching gives you set of edges that assures you that each vertice is connected with an edge only with one other vertice or no vertices. This set of vertices (from edges included in max matching) gives you also answer to VC problem - but its 2-approximation, cause in the worst case you can select 2 times bigger set of vertices than optimal one. – ShaQ Feb 01 '11 at 21:47