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 i-to-j 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....
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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