Connect K best to the introductory chapters.

diff --git a/dyn.tex b/dyn.tex
index e7432fca64e7604960cbd43e8afd8dc0785015dc..7197b22b68b2e8cd77515bc49c8ec3d6a180589b 100644 (file)
--- a/dyn.tex
+++ b/dyn.tex
@@ -957,5 +957,8 @@ to $\O(Km^{1/2})$ and improving Theorem \ref{kbestthm} to $\O(m\timesalpha(m,n)
 chapter could be modified to bring the complexity of finding the next tree down
 to polylogarithmic.
 
+\paran{Multiple minimum trees}%
+Another nice application of Theorem \ref{kbestthm} is finding all minimum spanning
+trees in a~graph that does not have distinct edge weights.
 
 \endpart

diff --git a/mst.tex b/mst.tex
index efc4d63238fe433e81007b922e78d9487b477198..1cf428e0ee78e05d1ad002def21227ecf16bf148 100644 (file)
--- a/mst.tex
+++ b/mst.tex
@@ -208,6 +208,9 @@ input, we will explicitly state so.
 In case the weights are not distinct, we can easily break ties by comparing some
 unique identifiers of edges. According to our characterization of minimum spanning
 trees, the unique MST of the new graph will still be a~MST of the original graph.
+Sometimes, we could be interested in finding all solutions, but as this is an~uncommon
+problem, we will postpone it until Section \ref{kbestsect}. For the time being,
+we will always assume distinct weights.
 
 \obs
 If all edge weights are distinct and $T$~is an~arbitrary tree, then for every tree~$T$ all edges are