Some more...

diff --git a/PLAN b/PLAN
index 40a1092ddea5d97ee7020649d129d1efabff2bd6..0bd1e9891d8685d2faa4704e849bb6878305038d 100644 (file)
--- a/PLAN
+++ b/PLAN
@@ -57,6 +57,7 @@ Spanning trees:
 - parallel algorithms: p243-cole (are there others?)
 - bounded expansion classes?
 - restricted cases and arborescences
+- verify: mention our simplifications
 
 Models:
 

diff --git a/adv.tex b/adv.tex
index dde5acbc42a7579909227d41599bb77c8ee0f2b3..b5c433b2bccb6a4f071221f34059b727ea39b702 100644 (file)
--- a/adv.tex
+++ b/adv.tex
@@ -783,10 +783,14 @@ of query paths in~$T$ (these are exactly the paths covered by the edges
 of $G\setminus T$). We use the reduction from Lemma \ref{verbranch} to get
 an~equivalent problem with a~full branching tree and a~set of parent-descendant
 paths. Then we run the \<FindHeavy> procedure (\ref{findheavy}) to find
-the heaviest edges and employ Lemma \ref{vercompares} to bound the number
+the heaviest edges and we employ Lemma \ref{vercompares} to bound the number
 of comparisons used.
 \qed
 
+\para
+We will now show an~efficient implementation of \<FindHeavy>, which will
+run in linear time on the RAM.
+