6.889: Algorithms for Planar Graphs and BeyondNovember 2, 2011Problem Set 8This 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 matrixAi. We sawthat performing a single iteration of Belamn-Ford amounts to finding all column minima ofAi, andshowed thatAican be partitioned into square Monge submatrices and that the column minima of am-by-nMonge matrix can be found inO(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 simplecycleC, and the length of an edge of the dense distance graph forGicorresponded to the length ofthe shortest path inGibetween the corresponding nodes ofC.In this problem we consider the case where the nodes of the dense distance graph lie on two simple cyclesinstead of just one. This case arises when using anr–decomposition instead of a single cycle to compute
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