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Unformatted text preview: 6.889: Algorithms for Planar Graphs and Beyond October 19, 2011 Problem Set 6 This problem set is due Wednesday, October 26 at noon. For this problem set it is important to know that the separation property is defined somewhat differently for contractionbidimensional problems. Let ( A,B,S ) be a separation of G and Z V ( G ) be an optimal solution to a contraction bidimensional problem in G . Let G A denote the graph obtained by contracting each connected component of G [ B ] into its adjacent vertex of S with smallest index, and define G B similarly. Let Z A denote an optimal solution to in G A and Z B and optimal solution in G B . We say has the separation property if  Z A   Z B  + O (  S  ) and  Z B   Z A  + O (  S  ) . 1. Show that the minimum connected dominating set problem admits a PTAS in apex minorfree graphs. A dominating set in a graph G is a set D V ( G ) such that D N ( D ) = V ( G ), where N ( D ) is the set of all vertices that are neighbors of some vertex of D . It is called a connected dominating set if G [ D ] is connected....
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This note was uploaded on 01/20/2012 for the course CS 6.889 taught by Professor Erikdemaine during the Fall '11 term at MIT.
 Fall '11
 ErikDemaine
 Algorithms

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