# ps8 - 6.889 Algorithms for Planar Graphs and Beyond...

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6.889: Algorithms for Planar Graphs and Beyond November 2, 2011 Problem Set 8 This problem set is due Wednesday, November 9 at noon. 1. Recall that in lecture 14 we represented the edges of the dense distance graph in a matrix A i . We saw that performing a single iteration of Belamn-Ford amounts to finding all column minima of A i , and showed that A i can be partitioned into square Monge submatrices and that the column minima of a m -by- n Monge matrix can be found in O ( m + n ) time using the SMAWK algorithm. In the case we discussed in class, the nodes of the dense distance graph were the nodes of a single simple cycle C , and the length of an edge of the dense distance graph for G i corresponded to the length of the shortest path in G i between the corresponding nodes of C . In this problem we consider the case where the nodes of the dense distance graph lie on two simple cycles instead of just one. This case arises when using an r –decomposition instead of a single cycle to compute
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