# LaTeX2HTML 97.1 (release) (July 13th, 1997)
# Associate images original text with physical files.


$key = q/{_inline}r_i(e){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img18.gif"
 ALT="$r\_i(e) $">|; 

$key = q/{figure}<verbatim_mark>verbatim7{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="711" HEIGHT="555"
 SRC="img41.gif"
 ALT="\begin{figure}
\begin{verbatim}
//**********************************************...
 ...******************************************************\end{verbatim}\end{figure}">|; 

$key = q/{_inline}r_j(e){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="47" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img19.gif"
 ALT="$ r\_j(e)$">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(defineg(graph'(123)'((12)(13)(31))))einline_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="526"
 SRC="img34.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...3\(\}\)
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}allttrelaxstaticPRIMITIVEGenRandomCmd(SCMn,SCMp)Graph*gr;if(!INTEGERP(n)",tc_subr_2,(PRIMITIVE(*)(...))GenRandomGraphCmd);relaxalltt{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="674" HEIGHT="427"
 SRC="img43.gif"
 ALT="\begin{figure}
\begin{alltt}
\relax
static PRIMITIVE GenRandomCmd(SCM n, SCM p)
...
 ...subr_2,
 (PRIMITIVE (*)(...))GenRandomGraphCmd);
}
\relax\end{alltt}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(defineh(graph'(123)'((1)(23)(123))))einline_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="253"
 SRC="img6.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...)\(\}\)
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(definems(mset-int3221))em_inline(#)_iinline_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="464"
 SRC="img22.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...3\(\}\)
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{_inline}n_mboxthis(e)-n_c(e))){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="20" HEIGHT="14" ALIGN="MIDDLE" BORDER="0"
 SRC="img73.gif"
 ALT="$n\_\mbox{this}(e) - n\_c(e)))$">|; 

$key = q/{figure}centerlineincludegraphics*[height=3in,width=4.5in]figuresdirectory_hier.ps{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="75" HEIGHT="33"
 SRC="img97.gif"
 ALT="\begin{figure}
\centerline{
\includegraphics 
*[height=3in,width=4.5in]{figures/directory_hier.ps}}\end{figure}">|; 

$key = q/{displaymath}lbrace[123]lbrace<12><13><23>rbracerbrace{displaymath}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="231" HEIGHT="29"
 SRC="img4.gif"
 ALT="\begin{displaymath}
\lbrace [1 2 3] \lbrace<1 2\gt <1 3\gt <2 3\gt\rbrace\rbrace \end{displaymath}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(definedg(digraph'(1234)'((123)(234)))inline_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="865"
 SRC="img35.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...4\(\}\)
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{_inline}1,ldots,n{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="75" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img78.gif"
 ALT="$1,\ldots,n$">|; 

$key = q/{_inline}E={e_0,e_2,ldots,e_m-1}{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="60" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img80.gif"
 ALT="$E = \{e_0, e_2, \ldots, e_{m-1}\}$">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(defineg(graph'(123)'((12)(13)(31))))em("black""black""black")relaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="209"
 SRC="img36.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ... ''black'' ''black'')} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim10vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="536"
 SRC="img45.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim30vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="536"
 SRC="img57.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim22vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="594" HEIGHT="380"
 SRC="img52.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim50vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="676" HEIGHT="449"
 SRC="img68.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim14vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="384"
 SRC="img48.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim42vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="458" HEIGHT="343"
 SRC="img64.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{_inline}mbox_inlinecol_inlinesubseteqmbox_inlinecol_2_inlinesubseteqmbox_inlinecol_k_inline{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="146" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img14.gif"
 ALT="$\mbox{$col$}\ \subseteq \mbox{$col_2$}\ \subseteq \mbox{$col_k$}\ $">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim70vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="576" HEIGHT="622"
 SRC="img88.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim34vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="567"
 SRC="img59.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim62vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="574" HEIGHT="497"
 SRC="img83.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim26vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="573" HEIGHT="341"
 SRC="img54.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim54vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="683" HEIGHT="557"
 SRC="img70.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim18vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="492"
 SRC="img50.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim46vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="427"
 SRC="img66.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim38vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="536"
 SRC="img61.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim66vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="471"
 SRC="img85.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim58vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="151" HEIGHT="33"
 SRC="img75.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(defines(set-int123))em_inline(#)_inliinline_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="526"
 SRC="img28.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...)\(\}\)
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}centerlineincludegraphics*[height=3in,width=4in]figurescollection_hier.ps{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="358"
 SRC="img62.gif"
 ALT="\begin{figure}
\centerline{
\includegraphics 
*[height=3in,width=4in]{figures/collection_hier.ps}}\end{figure}">|; 

$key = q/{_inline}s[i]ldotss[j]{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="95" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img77.gif"
 ALT="$s[i] \ldots s[j]$">|; 

$key = q/{figure}allttrelaxUBinGraph*GenRandom(intn,intp)UBinGraph*graph=newUBinGraph();gEdge*edge=graph->addEdge(s);s.clear();returngraph;relaxalltt{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="573" HEIGHT="469"
 SRC="img42.gif"
 ALT="\begin{figure}
\begin{alltt}
\relax
UBinGraph*
GenRandom(int n, int p)
{
 UBinGr...
 ...\gt addEdge(s);
 s.clear();
 }
 }
 return graph;
}
\relax\end{alltt}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(definev3(vector-copyv))em***Error:vecval=[]_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="464"
 SRC="img32.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...al = []
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}centerlineincludegraphics*[height=2in,width=3in]figureselementOps.ps{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="344" HEIGHT="228"
 SRC="img46.gif"
 ALT="\begin{figure}
\centerline{
\includegraphics 
*[height=2in,width=3in]{figures/elementOps.ps}}\end{figure}">|; 

$key = q/{_inline}mbox_inlinecol_i_inlinecupmbox_inlinecol_j_inline{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="88" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img17.gif"
 ALT="$\mbox{$col_i$}\ \cup \mbox{$col_j$}\ $">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(describev)em_inline(#)_inline[_inlinenumberinacomparison:(ab)relaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="719"
 SRC="img33.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...n a comparison: (a b)} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{_inline}mbox_inlineset_inline{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="31" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img21.gif"
 ALT="$\mbox{$set$}\ $">|; 

$key = q/{_inline}n_r(e)){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="73" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img72.gif"
 ALT="$n\_r(e))$">|; 

$key = q/{_inline}V'subseteqV{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="74" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img87.gif"
 ALT="$V' \subseteq V$">|; 

$key = q/{_inline}imbox_inline<_inlinej{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="36" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$i \mbox{$<$}\ j$">|; 

$key = q/{_inline}V={v_0,v_1,ldots,v_n-1}{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="78" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img79.gif"
 ALT="$V = \{v_0, v_1,\ldots, v_{n-1}\}$">|; 

$key = q/{_inline}Delta(g){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img38.gif"
 ALT="$\Delta(g)$">|; 

$key = q/{_inline}ldots{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="23" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img2.gif"
 ALT="$\ldots$">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(describev)em_inline(#)_inline[_inlinelttallttrelaxSTk>bflem()relaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="315"
 SRC="img31.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...k\gt {\bf l }{\em{
()} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(defineg(graph))em_inline(#)_inline[uninline_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="253"
 SRC="img5.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...)\(\}\)
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{_inline}rightarrow{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="28" HEIGHT="24" ALIGN="BOTTOM" BORDER="0"
 SRC="img98.gif"
 ALT="$\rightarrow$">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(defineg(graph'(123)'((12)(13)(31))))e)em("black""red""black")relaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="250"
 SRC="img37.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...'' ''red'' ''black'')} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(define-genericf)em_inline(#)_inline[uline(>)_inline4022e340])relaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="481"
 SRC="img26.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...t\)\(\gt\) 4022e340])} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}allttrelax#include<LINKpersalgorithmSTkInit.h>voidgen_Animation_Wrapper(riangles_Wrapper();voidSTk_algorithm_cleanup(void)relaxalltt{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="455" HEIGHT="730"
 SRC="img44.gif"
 ALT="\begin{figure}
\begin{alltt}
\relax
 ... ">|; 

$key = q/{_inline}O(logn){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="82" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img56.gif"
 ALT="$O(\log n)$">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(vector-int?v)em_inline(#)_inlinetrela?v2)em_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="291"
 SRC="img30.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (v...
 ... }{\em{
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{_inline}(0ldotsm-1){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="121" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="img92.gif"
 ALT="$(0\ldots m-1)$">|; 

$key = q/{_inline}(0ldotsn-1){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="108" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img91.gif"
 ALT="$(0\ldots n-1)$">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(defineg(graph'(123)'((12)(23)(31))))einline_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="399"
 SRC="img7.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...)\(\}\)
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(definems(mset-int1223))em_inline(#)_iinline_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="337"
 SRC="img24.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...3\(\}\)
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}centerlineincludegraphics*[height=3in,width=4.5in]figuresgraph_hier.ps{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="92" HEIGHT="33"
 SRC="img95.gif"
 ALT="\begin{figure}
\centerline{
\includegraphics 
*[height=3in,width=4.5in]{figures/graph_hier.ps}}\end{figure}">|; 

$key = q/{_inline}(rightarrow){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="36" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="img71.gif"
 ALT="\(\rightarrow\)">|; 

$key = q/{_inline}{w:(wine)wedge(wneqv)}{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="173" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img82.gif"
 ALT="$\{w : (w \in e) \wedge (w \neq v)\}$">|; 

$key = q/{_inline}O(llogn){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="90" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img93.gif"
 ALT="$O(l\log n)$">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim12vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="471"
 SRC="img47.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim40vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="514"
 SRC="img63.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim32vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="67" HEIGHT="33"
 SRC="img58.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim60vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="171" HEIGHT="33"
 SRC="img81.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim52vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="628" HEIGHT="579"
 SRC="img69.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim16vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="536"
 SRC="img49.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim44vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="567" HEIGHT="557"
 SRC="img65.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(definev(vector-int10))em_inline(#)_inval=[]_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="613"
 SRC="img29.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...al = []
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim36vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="574" HEIGHT="544"
 SRC="img60.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim72vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="59" HEIGHT="33"
 SRC="img89.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim28vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="492"
 SRC="img55.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{_inline}mbox_inlinecol_i_inlinesubsetmbox_inlinecol_j_inline{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="92" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img16.gif"
 ALT="$\mbox{$col_i$}\ \subset \mbox{$col_j$}\ $">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim64vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="182" HEIGHT="33"
 SRC="img84.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim56vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="57" HEIGHT="33"
 SRC="img74.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim48vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="649" HEIGHT="606"
 SRC="img67.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(definem(list->mset-int'(1223)))em_inlinline_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="675"
 SRC="img23.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...\(\gt\)
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{_inline}mbox_inlineset_inline,{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="30" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img20.gif"
 ALT="$\mbox{$set$},$">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim76vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="97" HEIGHT="33"
 SRC="img96.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushleftminipage[t]textwidthhrulefillvspace*-5mm<verbatim_mark>verbatimerbatim_mark>verbatim68vspace*-6mmhrulefillminipageflushleft{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="492"
 SRC="img86.gif"
 ALT="\begin{figure}
\begin{flushleft}
\begin{minipage}[t]
{\textwidth}
\hrulefill

\v...
 ...nd{verbatim}
\vspace*{-6mm}

\hrulefill\end{minipage}\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(defineg(graph'(1234)'((12)(13)(14))))ttrelaxSTk>bf(deltag)em3relaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="440"
 SRC="img39.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...bf (delta g) }{\em{
3} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(definems(mset-int1223))em_inline(#)_iqms)em_inline(#)_inlinetrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="416"
 SRC="img25.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ... }{\em{
\(\char93 \)t} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(add-vertex!1g)em_inline(#)_inline[_ininline_inline(#)_inlinefrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="377"
 SRC="img8.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (a...
 ...)\(\}\)
\(\char93 \)f} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{displaymath}lbrace[123]lbracelbrace12rbracelbrace13rbracelbrace23rbracerbracerbrace{displaymath}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="172" HEIGHT="29"
 SRC="img3.gif"
 ALT="\begin{displaymath}
\lbrace [1 2 3] \lbrace \lbrace1 2\rbrace \lbrace1 3\rbrace \lbrace2 3\rbrace\rbrace\rbrace \end{displaymath}">|; 

$key = q/{figure}flushlefthrulefillallttrelaxSTk>bf(definems(mset-int3221))em_inline(#)_iet-lesseq))emseq-greaterrelaxalltthrulefillflushleft{figure}MSF=1.6;FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="556" HEIGHT="250"
 SRC="img27.gif"
 ALT="\begin{figure}
\begin{flushleft}
\hrulefill

\begin{alltt}
\relax
STk\gt {\bf (d...
 ...)) }{\em{
seq-greater} }
\relax\end{alltt}
\hrulefill\end{flushleft}\end{figure}">|; 

$key = q/{_inline}winV(g){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="89" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img94.gif"
 ALT="$w \in V(g)$">|; 

$key = q/{_inline}imbox_inline<=_inlinej{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="50" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$i \mbox{$<=$}\ j$">|; 

$key = q/{_inline}imbox_inline>=_inlinej{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="50" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$i \mbox{$\gt=$}\ j$">|; 

$key = q/{figure}centerlineincludegraphics*[width=5.5in]dfs.psvspace*3mmcenterlineincludegraphics*[width=5.5in]titlepage_stk.ps{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="582" HEIGHT="552"
 SRC="img1.gif"
 ALT="\begin{figure}
\centerline{
\includegraphics 
*[width=5.5in]{dfs.ps}}
\vspace*{3mm}
\centerline{
\includegraphics 
*[width=5.5in]{titlepage_stk.ps}}\end{figure}">|; 

$key = q/{_inline}mboxthis-_inline>_inlinesize(){_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="106" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img76.gif"
 ALT="$ \mbox{this-$\gt$size()}$">|; 

$key = q/{_inline}mbox_inlinecol_inlinesubsetmbox_inlinecol_2_inlinesubsetmbox_inlinecol_k_inline,{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="151" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img15.gif"
 ALT="$\mbox{$col$}\ \subset \mbox{$col_2$}\ \subset \mbox{$col_k$}\ ,$">|; 

$key = q/{_inline}imbox_inline>_inlinej{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="36" HEIGHT="27" ALIGN="MIDDLE" BORDER="0"
 SRC="img12.gif"
 ALT="$i \mbox{$\gt$}\ j$">|; 

$key = q/{_inline}Vchoose2{_inline}MSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="28" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$V \choose 2$">|; 

$key = q/{figure}<verbatim_mark>verbatim6{figure}FSF=1.6;AAT;/;
$cached_env_img{$key} = q|<IMG WIDTH="637" HEIGHT="335"
 SRC="img40.gif"
 ALT="\begin{figure}
\begin{verbatim}
 ... ">|; 

1;

