From: Martin Mares <mj@ucw.cz>
Date: Sat, 19 Apr 2008 15:41:38 +0000 (+0200)
Subject: Unified yardsticks.
X-Git-Tag: printed~74
X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=3064137808233f772a75f3367c029ecde806455b;p=saga.git

Unified yardsticks.
---

diff --git a/PLAN b/PLAN
index 723d98b..e333a50 100644
--- a/PLAN
+++ b/PLAN
@@ -73,7 +73,6 @@ Related:
 Models:
 
 - add references to the C language
-- PM: unify yardsticks
 - all data structures should mention space complexity
 
 Ranking:
diff --git a/opt.tex b/opt.tex
index 98464e9..632fd4e 100644
--- a/opt.tex
+++ b/opt.tex
@@ -482,7 +482,8 @@ Every manipulation with ranks performed by the soft heap operations can be
 implemented on the Pointer Machine in constant amortized time.
 
 \proof
-We create a~``yardstick'' --- a~double linked list whose elements represent the possible
+We will recycle the idea of ``yardsticks'' from Section \ref{bucketsort}.
+We create a~yardstick --- a~doubly linked list whose elements represent the possible
 values of a~rank. Every vertex of a~queue will store its rank as a~pointer to
 the corresponding ``tick'' of the yardstick. We will extend the list as necessary.
 
@@ -1057,7 +1058,7 @@ algorithm runs on it in linear time.
 
 The combined graph~$G_B$ has~$n$ vertices, but less than~$n$ edges from the
 individual spanning trees and at most~$m/4$ additional edges which were
-corrupted. The iterations of the Bor\o{u}vka's algorithm on~$G_B$ take $\O(m)$
+corrupted. The Bor\o{u}vka steps on~$G_B$ take $\O(m)$
 time by Lemma \ref{boruvkaiter} and they produce a~graph~$G_C$ with at most~$n/4$
 vertices and at most $n/4 + m/4 \le m/2$ edges. (The $n$~tree edges in~$G_B$ are guaranteed
 to be reduced by the Bor\o{u}vka's algorithm.) It is easy to verify that this