ps2 - of G is a decomposition into O ( n/ ) vertex-disjoint...

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6.889: Algorithms for Planar Graphs and Beyond September 21, 2011 Problem Set 2 This problem set is due Wednesday, September 28 at noon. 1. Prove that any undirected planar graph G with non-negative edge weights can be transformed into an undirected planar graph G 0 with maximum degree 3 such that, for any u,v V ( G ), d G ( u,v ) = d G 0 ( f ( u ) ,f ( v )), where f : V ( G ) V ( G 0 ) maps vertices between G and G 0 ; and • | V ( G 0 ) | = O ( | V ( G ) | ). 2. A ρ –clustering
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Unformatted text preview: of G is a decomposition into O ( n/ ) vertex-disjoint connected pieces , each with ( ) vertices. Recall that a clustering, if computed eciently, can be used to compute an r division in o ( n log n ) time. Give a linear-time algorithm to compute a clustering for any graph with maximum degree three....
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