Notation.

diff --git a/PLAN b/PLAN
index c75cc05cab1fb7d1d512024a5effa9a9eb582c86..9b562ec5a872da4e346225212f9020f0d59bc912 100644 (file)
--- a/PLAN
+++ b/PLAN
@@ -66,7 +66,6 @@ Models:
 - mention in-place radix-sorting?
 - consequences of Q-Heaps: Thorup's undirected SSSP etc.
 - add more context from thorup:aczero, also mention FP operations
-- update notation.tex
 
 Ranking:
 

diff --git a/notation.tex b/notation.tex
index 4b15cad4bebaa34b31dc45047059209a8f512930..bbf7a534dbffe9efe73238de1c65bacfe5a87d6d 100644 (file)
--- a/notation.tex
+++ b/notation.tex
@@ -47,6 +47,7 @@
 \n{$\(x)$}{number~$x\in{\bb N}$ written in binary \[bitnota]}
 \n{$\(x)_b$}{$\(x)$ zero-padded to exactly $b$ bits \[bitnota]}
 \n{$x[i]$}{when $x\in{\bb N}$: the value of the $i$-th bit of~$x$ \[bitnota]}
+\n{$x[B]$}{when $x\in{\bb N}$: the values of the bits at positions in the set~$B$ \[qhnota]}
 \n{$\pi[i]$}{when $\pi$ is a~sequence: the $i$-th element of~$\pi$, starting with $\pi[1]$ \[brackets]}
 \n{$\pi[i\ldots j]$}{the subsequence $\pi[i], \pi[i+1], \ldots, \pi[j]$}
 \n{$\sigma^k$}{the string~$\sigma$ repeated $k$~times \[bitnota]}

diff --git a/ram.tex b/ram.tex
index ef84a21c1c0608441fedaec6ac6aa81cea87ff66..824382ef6e0bcc619677bb4b6d96ec6ae13e6fd8 100644 (file)
--- a/ram.tex
+++ b/ram.tex
@@ -799,7 +799,7 @@ must lie in the left subtree of the root and $x_{i+1},\ldots,x_n$ in its
 right subtree. Both subtrees can be then constructed recursively.\foot{This
 construction is also known as the \df{cartesian tree} for the sequence
 $g_1,\ldots,g_n$ and it is useful in many other algorithms as it can be
-constructed in $\O(n)$ time. A~nice application on the Lowest Common Ancestor
+built in $\O(n)$ time. A~nice application on the Lowest Common Ancestor
 and Range Minimum problems has been described by Bender et al.~in \cite{bender:lca}.}
 \qed
 
@@ -808,7 +808,7 @@ Unfortunately, the vector of the $g_i$'s is also too long (is has $k\log W$ bits
 and we have no upper bound on~$W$ in terms of~$k$), so we will compress it even
 further:
 
-\nota
+\nota\id{qhnota}%
 \itemize\ibull
 \:$B = \{g_1,\ldots,g_n\}$ --- the set of bit positions of all the guides, stored as a~sorted array,
 \:$G : \{1,\ldots,n\} \rightarrow \{1,\ldots,n\}$ --- a~function mapping