Unformatted text preview: T that end at C 2 , respectively. It is not hard to see that for every i ∈ C 1 and j ∈ C 2 , there exists a shortest itoj path in G that does not cross both P ‘ and P r . Let A ‘ and A r be the dense distance matrices that correspond to the graphs obtained by cutting G open along P ‘ and P r , respectively. Both A ‘ and A r are Monge, and A i,j ≤ A ‘ i,j and A i,j ≤ A r i,j . It follows that the column minima of A are the minimum between the column minima of A ‘ and A r which can be found in O (  C 1  +  C 2  ) time each using SMAWK....
View
Full
Document
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

Click to edit the document details