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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 BelamnFord 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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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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