[LON-CAPA-cvs] cvs: doc /lonnavdocs depth.eps navmaps.dia navmapsdocs.pdf navmapsdocs.tex simple.branch.eps tdv.vals.eps

Fri, 15 Nov 2002 17:29:04 -0000

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--bowersj21037381344
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bowersj2		Fri Nov 15 12:29:04 2002 EDT

  Added files:                 
    /doc/lonnavdocs	depth.eps navmaps.dia navmapsdocs.pdf 
                   	navmapsdocs.tex simple.branch.eps tdv.vals.eps 
  Log:
  Documentation on the algorithm used in lonnavmaps.

--bowersj21037381344
Content-Type: text/plain
Content-Disposition: attachment; filename="bowersj2-20021115122904.txt"

Index: doc/lonnavdocs/depth.eps
+++ doc/lonnavdocs/depth.eps
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cleartomark

%%EndResource
%%BeginResource: font LuxiSans
%!PS-AdobeFont-1.0: LuxiSans 1.1000
%%CreationDate: Mon Nov 12 2001
% Copyright Copyright (c) 2001 by Bigelow & Holmes Inc. Instructions copyright (c) 2001 by URW++.
% Copyright (c) 2001 by Bigelow & Holmes Inc. Instructions copyright (c) 2001 by URW++.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.1000) readonly def
/Notice (Copyright (c) 2001 by Bigelow & Holmes Inc. Instructions copyright (c) 2001 by URW++.) readonly def
/Copyright (Copyright Copyright (c) 2001 by Bigelow & Holmes Inc. Instructions copyright (c) 2001 by URW++.) readonly def
/FullName (Luxi Sans Regular) readonly def
/FamilyName (Luxi Sans) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0.0 def
/isFixedPitch false def
/UnderlinePosition -36 def
/UnderlineThickness 72 def
end readonly def
/FontName /LuxiSans def
/PaintType 0 def
/WMode 0 def
/FontBBox {-215 -211 988 993} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding 256 array 
0 1 255 {1 index exch /.notdef put} for 
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 198 /AE put
dup 140 /OE put
dup 216 /Oslash put
dup 196 /Adieresis put
dup 193 /Aacute put
dup 192 /Agrave put
dup 194 /Acircumflex put
dup 195 /Atilde put
dup 197 /Aring put
dup 199 /Ccedilla put
dup 208 /Eth put
dup 203 /Edieresis put
dup 201 /Eacute put
dup 200 /Egrave put
dup 202 /Ecircumflex put
dup 207 /Idieresis put
dup 205 /Iacute put
dup 204 /Igrave put
dup 206 /Icircumflex put
dup 209 /Ntilde put
dup 214 /Odieresis put
dup 211 /Oacute put
dup 210 /Ograve put
dup 212 /Ocircumflex put
dup 213 /Otilde put
dup 138 /Scaron put
dup 220 /Udieresis put
dup 218 /Uacute put
dup 217 /Ugrave put
dup 219 /Ucircumflex put
dup 221 /Yacute put
dup 222 /Thorn put
dup 159 /Ydieresis put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 230 /ae put
dup 156 /oe put
dup 248 /oslash put
dup 223 /germandbls put
dup 228 /adieresis put
dup 225 /aacute put
dup 224 /agrave put
dup 226 /acircumflex put
dup 227 /atilde put
dup 229 /aring put
dup 231 /ccedilla put
dup 235 /edieresis put
dup 233 /eacute put
dup 232 /egrave put
dup 234 /ecircumflex put
dup 239 /idieresis put
dup 237 /iacute put
dup 236 /igrave put
dup 238 /icircumflex put
dup 241 /ntilde put
dup 246 /odieresis put
dup 243 /oacute put
dup 242 /ograve put
dup 244 /ocircumflex put
dup 245 /otilde put
dup 154 /scaron put
dup 252 /udieresis put
dup 250 /uacute put
dup 249 /ugrave put
dup 251 /ucircumflex put
dup 253 /yacute put
dup 240 /eth put
dup 254 /thorn put
dup 255 /ydieresis put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 48 /zero put
dup 163 /sterling put
dup 36 /dollar put
dup 162 /cent put
dup 131 /florin put
dup 128 /Euro put
dup 165 /yen put
dup 185 /onesuperior put
dup 178 /twosuperior put
dup 179 /threesuperior put
dup 46 /period put
dup 58 /colon put
dup 133 /ellipsis put
dup 44 /comma put
dup 59 /semicolon put
dup 145 /quoteleft put
dup 148 /quotedblright put
dup 147 /quotedblleft put
dup 132 /quotedblbase put
dup 33 /exclam put
dup 161 /exclamdown put
dup 63 /question put
dup 191 /questiondown put
dup 187 /guillemotright put
dup 171 /guillemotleft put
dup 155 /guilsinglright put
dup 139 /guilsinglleft put
dup 47 /slash put
dup 45 /hyphen put
dup 173 /sfthyphen put
dup 150 /endash put
dup 151 /emdash put
dup 40 /parenleft put
dup 41 /parenright put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 38 /ampersand put
dup 167 /section put
dup 134 /dagger put
dup 135 /daggerdbl put
dup 42 /asterisk put
dup 39 /quotesingle put
dup 34 /quotedbl put
dup 64 /at put
dup 35 /numbersign put
dup 176 /degree put
dup 43 /plus put
dup 215 /multiply put
dup 247 /divide put
dup 61 /equal put
dup 153 /trademark put
dup 182 /paragraph put
dup 164 /currency put
dup 130 /quotesinglbase put
dup 146 /quoteright put
dup 123 /braceleft put
dup 125 /braceright put
dup 170 /ordfeminine put
dup 186 /ordmasculine put
dup 177 /plusminus put
dup 189 /onehalf put
dup 188 /onequarter put
dup 190 /threequarters put
dup 37 /percent put
dup 137 /perthousand put
dup 92 /backslash put
dup 168 /dieresis put
dup 180 /acute put
dup 96 /grave put
dup 136 /circumflex put
dup 152 /tilde put
dup 184 /cedilla put
dup 169 /copyright put
dup 174 /registered put
dup 32 /space put
dup 160 /nbspace put
dup 149 /bullet put
dup 60 /less put
dup 62 /greater put
dup 172 /logicalnot put
dup 94 /asciicircum put
dup 124 /bar put
dup 166 /brokenbar put
dup 95 /underscore put
dup 126 /asciitilde put
dup 181 /mu put
readonly def
/UniqueID 5078987 def
currentdict end
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Index: doc/lonnavdocs/navmaps.dia
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Index: doc/lonnavdocs/navmapsdocs.tex
+++ doc/lonnavdocs/navmapsdocs.tex
%% LyX 1.2 created this file.  For more info, see http://www.lyx.org/.
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\begin{document}

\title{Navigation Maps Iterator Algorithm}

\title{Jeremy Bowers}

\maketitle
As part of re-doing the Navigation Maps screen for LON-CAPA, I created an
iterator for traversing the maps. Since I'm not going to be around forever,
I wanted to document the most subtle part of the the algorithm I developed,
so later people don't need to read my mind. Since I wanted to use pictures,
that rules out trying to do it all in comments.

%
\begin{figure}
\begin{center}\includegraphics[  height=2in,
  keepaspectratio]{simple.branch.eps}\end{center}

\caption{\label{simple branches}Simple Branching Nav Map}
\end{figure}
In particular, the handling of branches is a challenge. So, suppose we have
the simple navigation map shown in figure \ref{simple branches}. As human
beings, we can look at that resource map and mentally represent that as the
following: \emph{Everybody sees resource A, then you have a choice of resources
B and C, or resources E and F, and everybody will do resource D}. We want
to represent that like this:

\begin{itemize}
\item A

\begin{itemize}
\item B or C
\item E or F
\end{itemize}
\item D
\end{itemize}
Or something like that. Actually, \LaTeX{} fails me here. At the very least,
I don't want a bullet in front of D, since that follows A, and in the real
nav maps, {}``B or C'' is represented in two rows, but you get the idea.

The problem is that the computer doesn't have the global, overall view we
get, and getting the computer to match our intuition is surprisingly difficult. 

If we consider the \emph{desired indentation depth} (or just \emph{depth}
for short) as what we are looking for, so we can display the navmaps correctly,
then we are looking for two things:

\begin{enumerate}
\item A mapping of the nodes to some depth.
\item A way of traversing the graph once the depth has been assigned.
\end{enumerate}

\section{Mapping The Nodes to Some Depth}

As I talk about the algorithm, markers like \textbf{{*}{*}1{*}{*}} will be
used to track the places in the source code that are being discussed.

Mapping the nodes to a depth is done via a two-pass algorithm (\textbf{{*}{*}1{*}{*}}).
The passes are virtually identical, but one starts from the top and one starts
from the bottom. 

The order the nodes are traversed in is not terribly importent, as long as
no node is encountered before one of its parent nodes have been encountered,
which is known to be true with this traversal (and most others, as well). 

For the top-down pass, we start with the first resource, and give it a {}``top-down-value''
(TDV for short) value of 0 (\textbf{{*}{*}2{*}{*}}). We then progress along
the links in some order, visiting resources and assigning them a value as
follows:

\begin{enumerate}
\item If the node we came from has only one link leaving it (i.e., this is the
only next node for that node), then this node is given the same TDV value
as the parent. (\textbf{{*}{*}3{*}{*}})
\item If the node we came from has more then one link leaving it, this node is
given the TDV value of the parent, plus one. (\textbf{{*}{*}4{*}{*}})
\item If we get to any given node through multiple paths, the minimal value is
taken. (See all uses of the {}``min'' function.)
\end{enumerate}
%
\begin{figure}
\begin{center}\includegraphics[  height=2in,
  keepaspectratio]{tdv.vals.eps}\end{center}

\caption{\label{TDV values figure}TDV Values}
\end{figure}
Using that algorithm on the given example navmap, we get the result shown
in figure \ref{TDV values figure}. \textbf{A} was given the value 0 to start
with. Each of \textbf{B} and \textbf{E} was given 1, because there are two
ways out of \textbf{A}. The rest of the resources were given the value 1
as well, because there is only one way out of the resources from that point
on.

%
\begin{figure}
\begin{center}\includegraphics[  height=2in,
  keepaspectratio]{depth.eps}\end{center}

\caption{\label{cap:Final-Depth-labels}Final Depth labels}
\end{figure}
Using the same algorithm on the link-reversed graph, starting at the finish
resource, we can do the same thing to get the {}``Bottom-Up-Values'' (BUV).
We can then take each node, and take the minimum of each value to get the
final Depth (D) value.. This is shown in figure \ref{cap:Final-Depth-labels}. 

\section{Traversing the graph}

Now that we've assigned desired depths, we need to figure out an order for
traversing the graph. I create a list of arrays, of the size of the maximum
depth, which I use to keep track of the links we need to keep track of. This
is stored in the variable \{STACK\}, which holds an array reference of array
references of that size. 

In the shown example, the maximum depth is two, so \$self->\{STACK\} will
be {[}{[}{]}, {[}{]}{]}. \textbf{A} and \textbf{D} will eventually end up
in the first array, \textbf{B}, \textbf{C}, \textbf{E}, and \textbf{F} will
be in the second. 

Basically, the procedure is this:

\begin{itemize}
\item Select the next resource to display.
\item Explore where that resource can get us, and store it in the stack.
\item Repeat until there are no more resources.
\end{itemize}
We start by priming the stack with the first resource to be examined, the
firstResource (\textbf{{*}{*}5{*}{*}}).

In order to select the next resource to display, we walk backwards along
the stack until we find the first non-empty list (\textbf{{*}{*}6{*}{*}}).
We pop the resource off that list, and that is the next resource (\textbf{{*}{*}7{*}{*}}).
This has the effect of following branches as quickly as possible, so that
we can guarentee that \textbf{B}, \textbf{C}, and \textbf{E}, \textbf{F}
will both be explored before \textbf{D}. \textbf{D} will not be selected
until the higher levels have been exhausted. 

Of course this works recursively, so it will work no matter how high the
level goes.

The only thing that needs a special case is when there are two branches,
as in the sample figure, and we get to the end of the first branch (\textbf{{*}{*}8{*}{*}}).
We can't detect the fact that the branch has ended just by looking at the
stack afterwards. So to remember that a branch has ended, detected when all
the potential next resources are of a lower level then the current resource,
even if there are no possible next resources, we push a marker onto the corresponding
stack that the branch has ended (\textbf{{*}{*}9{*}{*}}). We have to push
a marker onto the stack, because we may still need to recursively explore
the last resource if it's a map.

And that's pretty much it; there's a lot of bookkeeping and stuff, but that's
the core.
\end{document}

Index: doc/lonnavdocs/simple.branch.eps
+++ doc/lonnavdocs/simple.branch.eps
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cleartomark

%%EndResource
%%BeginResource: font LuxiSans
%!PS-AdobeFont-1.0: LuxiSans 1.1000
%%CreationDate: Mon Nov 12 2001
% Copyright Copyright (c) 2001 by Bigelow & Holmes Inc. Instructions copyright (c) 2001 by URW++.
% Copyright (c) 2001 by Bigelow & Holmes Inc. Instructions copyright (c) 2001 by URW++.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.1000) readonly def
/Notice (Copyright (c) 2001 by Bigelow & Holmes Inc. Instructions copyright (c) 2001 by URW++.) readonly def
/Copyright (Copyright Copyright (c) 2001 by Bigelow & Holmes Inc. Instructions copyright (c) 2001 by URW++.) readonly def
/FullName (Luxi Sans Regular) readonly def
/FamilyName (Luxi Sans) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0.0 def
/isFixedPitch false def
/UnderlinePosition -36 def
/UnderlineThickness 72 def
end readonly def
/FontName /LuxiSans def
/PaintType 0 def
/WMode 0 def
/FontBBox {-215 -211 988 993} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding 256 array 
0 1 255 {1 index exch /.notdef put} for 
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 198 /AE put
dup 140 /OE put
dup 216 /Oslash put
dup 196 /Adieresis put
dup 193 /Aacute put
dup 192 /Agrave put
dup 194 /Acircumflex put
dup 195 /Atilde put
dup 197 /Aring put
dup 199 /Ccedilla put
dup 208 /Eth put
dup 203 /Edieresis put
dup 201 /Eacute put
dup 200 /Egrave put
dup 202 /Ecircumflex put
dup 207 /Idieresis put
dup 205 /Iacute put
dup 204 /Igrave put
dup 206 /Icircumflex put
dup 209 /Ntilde put
dup 214 /Odieresis put
dup 211 /Oacute put
dup 210 /Ograve put
dup 212 /Ocircumflex put
dup 213 /Otilde put
dup 138 /Scaron put
dup 220 /Udieresis put
dup 218 /Uacute put
dup 217 /Ugrave put
dup 219 /Ucircumflex put
dup 221 /Yacute put
dup 222 /Thorn put
dup 159 /Ydieresis put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 230 /ae put
dup 156 /oe put
dup 248 /oslash put
dup 223 /germandbls put
dup 228 /adieresis put
dup 225 /aacute put
dup 224 /agrave put
dup 226 /acircumflex put
dup 227 /atilde put
dup 229 /aring put
dup 231 /ccedilla put
dup 235 /edieresis put
dup 233 /eacute put
dup 232 /egrave put
dup 234 /ecircumflex put
dup 239 /idieresis put
dup 237 /iacute put
dup 236 /igrave put
dup 238 /icircumflex put
dup 241 /ntilde put
dup 246 /odieresis put
dup 243 /oacute put
dup 242 /ograve put
dup 244 /ocircumflex put
dup 245 /otilde put
dup 154 /scaron put
dup 252 /udieresis put
dup 250 /uacute put
dup 249 /ugrave put
dup 251 /ucircumflex put
dup 253 /yacute put
dup 240 /eth put
dup 254 /thorn put
dup 255 /ydieresis put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 48 /zero put
dup 163 /sterling put
dup 36 /dollar put
dup 162 /cent put
dup 131 /florin put
dup 128 /Euro put
dup 165 /yen put
dup 185 /onesuperior put
dup 178 /twosuperior put
dup 179 /threesuperior put
dup 46 /period put
dup 58 /colon put
dup 133 /ellipsis put
dup 44 /comma put
dup 59 /semicolon put
dup 145 /quoteleft put
dup 148 /quotedblright put
dup 147 /quotedblleft put
dup 132 /quotedblbase put
dup 33 /exclam put
dup 161 /exclamdown put
dup 63 /question put
dup 191 /questiondown put
dup 187 /guillemotright put
dup 171 /guillemotleft put
dup 155 /guilsinglright put
dup 139 /guilsinglleft put
dup 47 /slash put
dup 45 /hyphen put
dup 173 /sfthyphen put
dup 150 /endash put
dup 151 /emdash put
dup 40 /parenleft put
dup 41 /parenright put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 38 /ampersand put
dup 167 /section put
dup 134 /dagger put
dup 135 /daggerdbl put
dup 42 /asterisk put
dup 39 /quotesingle put
dup 34 /quotedbl put
dup 64 /at put
dup 35 /numbersign put
dup 176 /degree put
dup 43 /plus put
dup 215 /multiply put
dup 247 /divide put
dup 61 /equal put
dup 153 /trademark put
dup 182 /paragraph put
dup 164 /currency put
dup 130 /quotesinglbase put
dup 146 /quoteright put
dup 123 /braceleft put
dup 125 /braceright put
dup 170 /ordfeminine put
dup 186 /ordmasculine put
dup 177 /plusminus put
dup 189 /onehalf put
dup 188 /onequarter put
dup 190 /threequarters put
dup 37 /percent put
dup 137 /perthousand put
dup 92 /backslash put
dup 168 /dieresis put
dup 180 /acute put
dup 96 /grave put
dup 136 /circumflex put
dup 152 /tilde put
dup 184 /cedilla put
dup 169 /copyright put
dup 174 /registered put
dup 32 /space put
dup 160 /nbspace put
dup 149 /bullet put
dup 60 /less put
dup 62 /greater put
dup 172 /logicalnot put
dup 94 /asciicircum put
dup 124 /bar put
dup 166 /brokenbar put
dup 95 /underscore put
dup 126 /asciitilde put
dup 181 /mu put
readonly def
/UniqueID 5078987 def
currentdict end
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