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diff --git a/images/16-ec-from-bs32-normalized.tex b/images/16-ec-from-bs32-normalized.tex
new file mode 100644 (file)
index 0000000..9585843
--- /dev/null
+++ b/images/16-ec-from-bs32-normalized.tex
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diff --git a/images/16-ec-from-bs32.tex b/images/16-ec-from-bs32.tex
new file mode 100644 (file)
index 0000000..e1bf1b5
--- /dev/null
+++ b/images/16-ec-from-bs32.tex
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+\path[comp] (v472) -- (v473);
+
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+\path[comp active maximum] (v474) -- (v475);
+
+\node[vertex inactive maximum] (v476) at (14.48,11.75) {};
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+\path[comp inactive maximum] (v476) -- (v477);
+
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+\node[vertex inactive maximum] (v479) at (14.48,13.01) {};
+\path[comp inactive maximum] (v478) -- (v479);
+
+\end{tikzpicture}

diff --git a/images/16-ec-from-ps32.tex b/images/16-ec-from-ps32.tex
index 9e94974..3d94d3a 100644 (file)
--- a/images/16-ec-from-ps32.tex
+++ b/images/16-ec-from-ps32.tex
@@ -1,270 +1,270 @@
-\begin{tikzpicture}[scale=0.60,auto]
-\node[vertex] (v0) at (1.50,0) {};
-\node[vertex] (v1) at (1.50,2) {};
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 \path[comp] (v0) -- (v1);
 
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diff --git a/images/16-pairwise.tex b/images/16-pairwise.tex
new file mode 100644 (file)
index 0000000..7de5dba
--- /dev/null
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deleted file mode 100644 (file)
index 485d6ed..0000000
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+++ /dev/null
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+\path[comp inactive minimum] (v288) -- (v289);
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+\path[comp inactive minimum] (v290) -- (v291);
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+\node[vertex inactive maximum] (v378) at (14.58,9.13) {};
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+\path[comp inactive maximum] (v380) -- (v381);
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+\end{tikzpicture}

diff --git a/images/gamma_dist.gnuplot b/images/gamma_dist.gnuplot
new file mode 100644 (file)
index 0000000..d62cace
--- /dev/null
+++ b/images/gamma_dist.gnuplot
@@ -0,0 +1,10 @@
+_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x
+pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)
+dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))
+gamma_offset = 0.0
+gamma_k = 15.7880378786862
+gamma_theta = 0.980078674752871
+gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)
+#gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma(gamma_k))
+#gamma_fit(x) = 100.0 * gamma_dist(x - gamma_offset)
+

diff --git a/images/markov-comparators-12-pct.data b/images/markov-comparators-12-pct.data
new file mode 100644 (file)
index 0000000..87d460b
--- /dev/null
+++ b/images/markov-comparators-12-pct.data
@@ -0,0 +1,41 @@
+41 0.091900
+42 0.347600
+43 1.120700
+44 3.481000
+45 7.939400
+46 12.061400
+47 14.087900
+48 13.914800
+49 11.997600
+50 9.773000
+51 7.513400
+52 5.488200
+53 3.909200
+54 2.752300
+55 1.899600
+56 1.255700
+57 0.835600
+58 0.531400
+59 0.357700
+60 0.242700
+61 0.143700
+62 0.090700
+63 0.063200
+64 0.039200
+65 0.023500
+66 0.013800
+67 0.009200
+68 0.005600
+69 0.003900
+70 0.003000
+71 0.001200
+72 0.000800
+73 0.000400
+74 0.000200
+75 0.000100
+76 0.000200
+77 0.000000
+78 0.000100
+79 0.000000
+80 0.000000
+81 0.000100

diff --git a/images/markov-comparators-12-pct.gnuplot b/images/markov-comparators-12-pct.gnuplot
new file mode 100644 (file)
index 0000000..718b7a0
--- /dev/null
+++ b/images/markov-comparators-12-pct.gnuplot
@@ -0,0 +1,166 @@
+#!/usr/bin/gnuplot -persist
+#
+#    
+#      G N U P L O T
+#      Version 4.4 patchlevel 0
+#      last modified March 2010
+#      System: Linux 2.6.32-5-amd64
+#    
+#      Copyright (C) 1986-1993, 1998, 2004, 2007-2010
+#      Thomas Williams, Colin Kelley and many others
+#    
+#      gnuplot home:     http://www.gnuplot.info
+#      faq, bugs, etc:   type "help seeking-assistance"
+#      immediate help:   type "help"
+#      plot window:      hit 'h'
+# set terminal wxt 0
+# set output
+unset clip points
+set clip one
+unset clip two
+set bar 1.000000 front
+set border 31 front linetype -1 linewidth 1.000
+set xdata
+set ydata
+set zdata
+set x2data
+set y2data
+set timefmt x "%d/%m/%y,%H:%M"
+set timefmt y "%d/%m/%y,%H:%M"
+set timefmt z "%d/%m/%y,%H:%M"
+set timefmt x2 "%d/%m/%y,%H:%M"
+set timefmt y2 "%d/%m/%y,%H:%M"
+set timefmt cb "%d/%m/%y,%H:%M"
+set boxwidth
+set style fill  empty border
+set style rectangle back fc  lt -3 fillstyle   solid 1.00 border lt -1
+set dummy x,y
+set format x "% g"
+set format y "% g"
+set format x2 "% g"
+set format y2 "% g"
+set format z "% g"
+set format cb "% g"
+set angles radians
+unset grid
+set key title ""
+set key inside right top vertical Right noreverse enhanced autotitles nobox
+set key noinvert samplen 4 spacing 1 width 0 height 0 
+unset label
+unset arrow
+set style increment default
+unset style line
+unset style arrow
+set style histogram clustered gap 2 title  offset character 0, 0, 0
+unset logscale
+set offsets 0, 0, 0, 0
+set pointsize 1
+set encoding default
+unset polar
+unset parametric
+unset decimalsign
+set view 60, 30, 1, 1  
+set samples 100, 100
+set isosamples 10, 10
+set surface
+unset contour
+set clabel '%8.3g'
+set mapping cartesian
+set datafile separator whitespace
+unset hidden3d
+set cntrparam order 4
+set cntrparam linear
+set cntrparam levels auto 5
+set cntrparam points 5
+set size ratio 0 1,1
+set origin 0,0
+set style data points
+set style function lines
+set xzeroaxis linetype -2 linewidth 1.000
+set yzeroaxis linetype -2 linewidth 1.000
+set zzeroaxis linetype -2 linewidth 1.000
+set x2zeroaxis linetype -2 linewidth 1.000
+set y2zeroaxis linetype -2 linewidth 1.000
+set ticslevel 0.5
+set mxtics default
+set mytics default
+set mztics default
+set mx2tics default
+set my2tics default
+set mcbtics default
+set xtics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set xtics autofreq  norangelimit
+set ytics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set ytics autofreq  norangelimit
+set ztics border in scale 1,0.5 nomirror norotate  offset character 0, 0, 0
+set ztics autofreq  norangelimit
+set nox2tics
+set noy2tics
+set cbtics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set cbtics autofreq  norangelimit
+set title "" 
+set title  offset character 0, 0, 0 font "" norotate
+set timestamp bottom 
+set timestamp "" 
+set timestamp  offset character 0, 0, 0 font "" norotate
+set rrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set trange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set urange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set vrange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set xlabel "Komparatoren" 
+set xlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set x2label "" 
+set x2label  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set xrange [ * : * ] noreverse nowriteback  # (currently [41.0000:81.0000] )
+set x2range [ * : * ] noreverse nowriteback  # (currently [41.0000:81.0000] )
+set ylabel "Prozent" 
+set ylabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set y2label "" 
+set y2label  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set yrange [ * : * ] noreverse nowriteback  # (currently [0.00000:16.0000] )
+set y2range [ * : * ] noreverse nowriteback  # (currently [0.00000:14.0879] )
+set zlabel "" 
+set zlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set zrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set cblabel "" 
+set cblabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set cbrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set zero 1e-08
+set lmargin  -1
+set bmargin  -1
+set rmargin  -1
+set tmargin  -1
+set locale "en_US.UTF-8"
+set pm3d explicit at s
+set pm3d scansautomatic
+set pm3d interpolate 1,1 flush begin noftriangles nohidden3d corners2color mean
+set palette positive nops_allcF maxcolors 0 gamma 1.5 color model RGB 
+set palette rgbformulae 7, 5, 15
+set colorbox default
+set colorbox vertical origin screen 0.9, 0.2, 0 size screen 0.05, 0.6, 0 front bdefault
+set loadpath 
+set fontpath 
+set fit noerrorvariables
+gamma_gamma(x) = (floor(x - 0.5))!
+gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma(gamma_k))
+gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)
+_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x
+pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)
+dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))
+GNUTERM = "wxt"
+GPFUN_gamma_gamma = "gamma_gamma(x) = (floor(x - 0.5))!"
+gamma_k = 8.26729758801638
+gamma_theta = 0.961930249498844
+GPFUN_gamma_dist = "gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma(gamma_k))"
+gamma_offset = 40
+GPFUN_gamma_fit = "gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)"
+FIT_CONVERGED = 1
+FIT_NDF = 39
+FIT_STDFIT = 0.222936770551606
+FIT_WSSR = 1.9383313428952
+GPFUN__ln_dgamma = "_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x"
+GPFUN_pgamma = "pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)"
+GPFUN_dgamma = "dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))"
+plot [x=41:81] './images/markov-comparators-12-pct.data' title 'Gemessene Daten', gamma_fit(x) title 'Gamma-Verteilung'
+## fit gamma_fit(x) 'images/markov-comparators-12-pct.data' via gamma_k, gamma_theta
+#    EOF

diff --git a/images/markov-comparators-14-pct.data b/images/markov-comparators-14-pct.data
new file mode 100644 (file)
index 0000000..dff3e84
--- /dev/null
+++ b/images/markov-comparators-14-pct.data
@@ -0,0 +1,49 @@
+53 0.023000
+54 0.076800
+55 0.346200
+56 0.985900
+57 2.245000
+58 4.447600
+59 7.318500
+60 9.956200
+61 11.628000
+62 11.749200
+63 11.005500
+64 9.528900
+65 7.816700
+66 6.207400
+67 4.703300
+68 3.507500
+69 2.525400
+70 1.839200
+71 1.300700
+72 0.882900
+73 0.621900
+74 0.421000
+75 0.288000
+76 0.193000
+77 0.132600
+78 0.082900
+79 0.055200
+80 0.038000
+81 0.025900
+82 0.016600
+83 0.012000
+84 0.006800
+85 0.004000
+86 0.002800
+87 0.001700
+88 0.001300
+89 0.000800
+90 0.000500
+91 0.000100
+92 0.000200
+93 0.000200
+94 0.000200
+95 0.000000
+96 0.000100
+97 0.000000
+98 0.000100
+99 0.000100
+100 0.000000
+101 0.000100

diff --git a/images/markov-comparators-14-pct.gnuplot b/images/markov-comparators-14-pct.gnuplot
new file mode 100644 (file)
index 0000000..d8a3937
--- /dev/null
+++ b/images/markov-comparators-14-pct.gnuplot
@@ -0,0 +1,162 @@
+#!/usr/bin/gnuplot -persist
+#
+#    
+#      G N U P L O T
+#      Version 4.4 patchlevel 0
+#      last modified March 2010
+#      System: Linux 2.6.32-5-amd64
+#    
+#      Copyright (C) 1986-1993, 1998, 2004, 2007-2010
+#      Thomas Williams, Colin Kelley and many others
+#    
+#      gnuplot home:     http://www.gnuplot.info
+#      faq, bugs, etc:   type "help seeking-assistance"
+#      immediate help:   type "help"
+#      plot window:      hit 'h'
+# set terminal wxt 0
+# set output
+unset clip points
+set clip one
+unset clip two
+set bar 1.000000 front
+set border 31 front linetype -1 linewidth 1.000
+set xdata
+set ydata
+set zdata
+set x2data
+set y2data
+set timefmt x "%d/%m/%y,%H:%M"
+set timefmt y "%d/%m/%y,%H:%M"
+set timefmt z "%d/%m/%y,%H:%M"
+set timefmt x2 "%d/%m/%y,%H:%M"
+set timefmt y2 "%d/%m/%y,%H:%M"
+set timefmt cb "%d/%m/%y,%H:%M"
+set boxwidth
+set style fill  empty border
+set style rectangle back fc lt -3 fillstyle   solid 1.00 border lt -1
+set dummy x,y
+set format x "% g"
+set format y "% g"
+set format x2 "% g"
+set format y2 "% g"
+set format z "% g"
+set format cb "% g"
+set angles radians
+unset grid
+set key title ""
+set key inside right top vertical Right noreverse enhanced autotitles nobox
+set key noinvert samplen 4 spacing 1 width 0 height 0 
+unset label
+unset arrow
+set style increment default
+unset style line
+unset style arrow
+set style histogram clustered gap 2 title  offset character 0, 0, 0
+unset logscale
+set offsets 0, 0, 0, 0
+set pointsize 1
+set encoding default
+unset polar
+unset parametric
+unset decimalsign
+set view 60, 30, 1, 1  
+set samples 100, 100
+set isosamples 10, 10
+set surface
+unset contour
+set clabel '%8.3g'
+set mapping cartesian
+set datafile separator whitespace
+unset hidden3d
+set cntrparam order 4
+set cntrparam linear
+set cntrparam levels auto 5
+set cntrparam points 5
+set size ratio 0 1,1
+set origin 0,0
+set style data points
+set style function lines
+set xzeroaxis linetype -2 linewidth 1.000
+set yzeroaxis linetype -2 linewidth 1.000
+set zzeroaxis linetype -2 linewidth 1.000
+set x2zeroaxis linetype -2 linewidth 1.000
+set y2zeroaxis linetype -2 linewidth 1.000
+set ticslevel 0.5
+set mxtics default
+set mytics default
+set mztics default
+set mx2tics default
+set my2tics default
+set mcbtics default
+set xtics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set xtics autofreq  norangelimit
+set ytics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set ytics autofreq  norangelimit
+set ztics border in scale 1,0.5 nomirror norotate  offset character 0, 0, 0
+set ztics autofreq  norangelimit
+set nox2tics
+set noy2tics
+set cbtics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set cbtics autofreq  norangelimit
+set title "" 
+set title  offset character 0, 0, 0 font "" norotate
+set timestamp bottom 
+set timestamp "" 
+set timestamp  offset character 0, 0, 0 font "" norotate
+set rrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set trange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set urange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set vrange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set xlabel "Komparatoren" 
+set xlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set x2label "" 
+set x2label  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set xrange [ * : * ] noreverse nowriteback  # (currently [53.0000:101.000] )
+set x2range [ * : * ] noreverse nowriteback  # (currently [53.0000:101.000] )
+set ylabel "Prozent" 
+set ylabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set y2label "" 
+set y2label  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set yrange [ * : * ] noreverse nowriteback  # (currently [0.00000:12.0000] )
+set y2range [ * : * ] noreverse nowriteback  # (currently [0.00000:11.7492] )
+set zlabel "" 
+set zlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set zrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set cblabel "" 
+set cblabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set cbrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set zero 1e-08
+set lmargin  -1
+set bmargin  -1
+set rmargin  -1
+set tmargin  -1
+set locale "en_US.UTF-8"
+set pm3d explicit at s
+set pm3d scansautomatic
+set pm3d interpolate 1,1 flush begin noftriangles nohidden3d corners2color mean
+set palette positive nops_allcF maxcolors 0 gamma 1.5 color model RGB 
+set palette rgbformulae 7, 5, 15
+set colorbox default
+set colorbox vertical origin screen 0.9, 0.2, 0 size screen 0.05, 0.6, 0 front bdefault
+set loadpath 
+set fontpath 
+set fit noerrorvariables
+_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x
+pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)
+dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))
+gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)
+GNUTERM = "wxt"
+GPFUN__ln_dgamma = "_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x"
+GPFUN_pgamma = "pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)"
+GPFUN_dgamma = "dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))"
+gamma_offset = 52
+gamma_k = 9.52243956215441
+gamma_theta = 0.866869465480136
+GPFUN_gamma_fit = "gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)"
+FIT_CONVERGED = 1
+FIT_NDF = 47
+FIT_STDFIT = 0.125963571262577
+FIT_WSSR = 0.745740600405454
+plot [x=53:101] 'images/markov-comparators-14-pct.data' title 'Gemessene Daten', gamma_fit(x) title 'Gamma-Verteilung'
+## fit gamma_fit(x) 'images/markov-comparators-14-pct.data' via gamma_k, gamma_theta
+#    EOF

diff --git a/images/markov-comparators-16-pct.data b/images/markov-comparators-16-pct.data
new file mode 100644 (file)
index 0000000..515fc83
--- /dev/null
+++ b/images/markov-comparators-16-pct.data
@@ -0,0 +1,54 @@
+63 0.00036
+64 0.00148
+65 0.00420
+66 0.01019
+67 0.03000
+68 0.06674
+69 0.18834
+70 0.45496
+71 1.01551
+72 2.08409
+73 3.92942
+74 6.10824
+75 8.35161
+76 9.88771
+77 10.63978
+78 10.38984
+79 9.52167
+80 8.31205
+81 6.89893
+82 5.57473
+83 4.35112
+84 3.31039
+85 2.47437
+86 1.82548
+87 1.33113
+88 0.95592
+89 0.68841
+90 0.48849
+91 0.33511
+92 0.23689
+93 0.16438
+94 0.11395
+95 0.08025
+96 0.05561
+97 0.03840
+98 0.02602
+99 0.01815
+100 0.01064
+101 0.00747
+102 0.00510
+103 0.00362
+104 0.00300
+105 0.00161
+106 0.00143
+107 0.00125
+108 0.00067
+109 0.00031
+110 0.00027
+111 0.00031
+112 0.00004
+113 0.00013
+114 0.00000
+115 0.00013
+116 0.00009

diff --git a/images/markov-comparators-16-pct.gnuplot b/images/markov-comparators-16-pct.gnuplot
new file mode 100644 (file)
index 0000000..0751469
--- /dev/null
+++ b/images/markov-comparators-16-pct.gnuplot
@@ -0,0 +1,219 @@
+#!/usr/bin/gnuplot -persist
+#
+#    
+#      G N U P L O T
+#      Version 4.4 patchlevel 0
+#      last modified March 2010
+#      System: Linux 2.6.32-5-amd64
+#    
+#      Copyright (C) 1986-1993, 1998, 2004, 2007-2010
+#      Thomas Williams, Colin Kelley and many others
+#    
+#      gnuplot home:     http://www.gnuplot.info
+#      faq, bugs, etc:   type "help seeking-assistance"
+#      immediate help:   type "help"
+#      plot window:      hit 'h'
+# set terminal wxt 0
+# set output
+unset clip points
+set clip one
+unset clip two
+set bar 1.000000 front
+set border 31 front linetype -1 linewidth 1.000
+set xdata
+set ydata
+set zdata
+set x2data
+set y2data
+set timefmt x "%d/%m/%y,%H:%M"
+set timefmt y "%d/%m/%y,%H:%M"
+set timefmt z "%d/%m/%y,%H:%M"
+set timefmt x2 "%d/%m/%y,%H:%M"
+set timefmt y2 "%d/%m/%y,%H:%M"
+set timefmt cb "%d/%m/%y,%H:%M"
+set boxwidth
+set style fill  empty border
+set style rectangle back fc  lt -3 fillstyle   solid 1.00 border lt -1
+set dummy x,y
+set format x "% g"
+set format y "% g"
+set format x2 "% g"
+set format y2 "% g"
+set format z "% g"
+set format cb "% g"
+set angles radians
+unset grid
+set key title ""
+set key inside right top vertical Right noreverse enhanced autotitles nobox
+set key noinvert samplen 4 spacing 1 width 0 height 0 
+unset label
+unset arrow
+set style increment default
+unset style line
+unset style arrow
+set style histogram clustered gap 2 title  offset character 0, 0, 0
+unset logscale
+set offsets 0, 0, 0, 0
+set pointsize 1
+set encoding default
+unset polar
+unset parametric
+unset decimalsign
+set view 60, 30, 1, 1  
+set samples 100, 100
+set isosamples 10, 10
+set surface
+unset contour
+set clabel '%8.3g'
+set mapping cartesian
+set datafile separator whitespace
+unset hidden3d
+set cntrparam order 4
+set cntrparam linear
+set cntrparam levels auto 5
+set cntrparam points 5
+set size ratio 0 1,1
+set origin 0,0
+set style data points
+set style function lines
+set xzeroaxis linetype -2 linewidth 1.000
+set yzeroaxis linetype -2 linewidth 1.000
+set zzeroaxis linetype -2 linewidth 1.000
+set x2zeroaxis linetype -2 linewidth 1.000
+set y2zeroaxis linetype -2 linewidth 1.000
+set ticslevel 0.5
+set mxtics default
+set mytics default
+set mztics default
+set mx2tics default
+set my2tics default
+set mcbtics default
+set xtics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set xtics autofreq  norangelimit
+set ytics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set ytics autofreq  norangelimit
+set ztics border in scale 1,0.5 nomirror norotate  offset character 0, 0, 0
+set ztics autofreq  norangelimit
+set nox2tics
+set noy2tics
+set cbtics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set cbtics autofreq  norangelimit
+set title "" 
+set title  offset character 0, 0, 0 font "" norotate
+set timestamp bottom 
+set timestamp "" 
+set timestamp  offset character 0, 0, 0 font "" norotate
+set rrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set trange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set urange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set vrange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set xlabel "Komparatoren" 
+set xlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set x2label "" 
+set x2label  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set xrange [ * : * ] noreverse nowriteback  # (currently [63.0000:116.000] )
+set x2range [ * : * ] noreverse nowriteback  # (currently [63.0000:116.000] )
+set ylabel "Prozent" 
+set ylabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set y2label "" 
+set y2label  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set yrange [ * : * ] noreverse nowriteback  # (currently [0.00000:12.0000] )
+set y2range [ * : * ] noreverse nowriteback  # (currently [0.00000:10.6398] )
+set zlabel "" 
+set zlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set zrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set cblabel "" 
+set cblabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set cbrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set zero 1e-08
+set lmargin  -1
+set bmargin  -1
+set rmargin  -1
+set tmargin  -1
+set locale "en_US.UTF-8"
+set pm3d explicit at s
+set pm3d scansautomatic
+set pm3d interpolate 1,1 flush begin noftriangles nohidden3d corners2color mean
+set palette positive nops_allcF maxcolors 0 gamma 1.5 color model RGB 
+set palette rgbformulae 7, 5, 15
+set colorbox default
+set colorbox vertical origin screen 0.9, 0.2, 0 size screen 0.05, 0.6, 0 front bdefault
+set loadpath 
+set fontpath 
+set fit noerrorvariables
+binom(n,k) = (n!) / ((k!) * ((n-k)!))
+binv(n,k,p) = binom(n,k) * (p**k) * ((1-p)**(n-k))
+bin(x) = binv(n,floor(x),p)
+gauss(x) = (a1 / sigma) * exp((-0.5) * ((x - mu) / sigma)**2.0)
+poisson_int(x) = exp((-1.0) * lambda) * (lambda**x) / (x!)
+poisson(x) = poisson_int(floor(x + 0.5))
+erl(x) = gamma * exp(-1.0 * gamma * x) * (gamma * x)**(n_erl - 1) / ((n_erl - 1)!)
+binomial_int(x) = binomial_coeff(n, x) * p**x * (1-p)**(n-x)
+binomial_coeff(n,k) = (n!) / ((k!) * ((n-k)!))
+binomial(x) = binomial_int(floor(x + 0.5))
+binomial_fit(x) = 100.0 * binomial(x-19.0)
+poisson_fit(x) = 100.0 * poisson(x - offset)
+gauss_fit(x) = 100.0 * gauss(x)
+cauchy(x) = (1.0 / pi) * s / (s**2.0 + (x - t)**2)
+cauchy_fit(x) = 100.0 * cauchy(x)
+erlang_fit(x) = 100.0 * erl(x - erl_offset)
+gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma(gamma_k))
+gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)
+foo_fit(x) = foo_a0 * exp(foo_a1 * (x - 62))
+_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x
+pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)
+dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))
+GNUTERM = "wxt"
+GPFUN_binom = "binom(n,k) = (n!) / ((k!) * ((n-k)!))"
+GPFUN_binv = "binv(n,k,p) = binom(n,k) * (p**k) * ((1-p)**(n-k))"
+n = 29
+p = 0.172562132555044
+GPFUN_bin = "bin(x) = binv(n,floor(x),p)"
+a1 = 0.398942280401433
+sigma = 1.88445909011715
+mu = 23.800757470569
+GPFUN_gauss = "gauss(x) = (a1 / sigma) * exp((-0.5) * ((x - mu) / sigma)**2.0)"
+lambda = 5.10554056666183
+GPFUN_poisson_int = "poisson_int(x) = exp((-1.0) * lambda) * (lambda**x) / (x!)"
+GPFUN_poisson = "poisson(x) = poisson_int(floor(x + 0.5))"
+gamma = 1.90073273091251
+n_erl = 54
+GPFUN_erl = "erl(x) = gamma * exp(-1.0 * gamma * x) * (gamma * x)**(n_erl - 1) / ((n_erl - 1)!)"
+GPFUN_binomial_int = "binomial_int(x) = binomial_coeff(n, x) * p**x * (1-p)**(n-x)"
+GPFUN_binomial_coeff = "binomial_coeff(n,k) = (n!) / ((k!) * ((n-k)!))"
+GPFUN_binomial = "binomial(x) = binomial_int(floor(x + 0.5))"
+GPFUN_binomial_fit = "binomial_fit(x) = 100.0 * binomial(x-19.0)"
+offset = 19
+GPFUN_poisson_fit = "poisson_fit(x) = 100.0 * poisson(x - offset)"
+GPFUN_gauss_fit = "gauss_fit(x) = 100.0 * gauss(x)"
+s = 1.39871428165847
+t = 23.5320369849105
+GPFUN_cauchy = "cauchy(x) = (1.0 / pi) * s / (s**2.0 + (x - t)**2)"
+GPFUN_cauchy_fit = "cauchy_fit(x) = 100.0 * cauchy(x)"
+erl_offset = 49.8425987940659
+GPFUN_erlang_fit = "erlang_fit(x) = 100.0 * erl(x - erl_offset)"
+gamma_k = 17.9390580825481
+gamma_theta = 1.09113152299828
+GPFUN_gamma_dist = "gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma_gamma(gamma_k))"
+gamma_offset = 62
+GPFUN_gamma_fit = "gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)"
+foo_a0 = 0.000540217815483465
+foo_a1 = 0.838098058527587
+GPFUN_foo_fit = "foo_fit(x) = foo_a0 * exp(foo_a1 * (x - 62))"
+y = 0
+FIT_CONVERGED = 1
+a = 240000
+a0 = 2.0
+FIT_NDF = 52
+FIT_STDFIT = 0.15913245106829
+FIT_WSSR = 1.31680312311609
+lamdba = 14.0
+scale = 5000000
+GPFUN_gamma_gamma = "gamma_gamma(x) = (floor(x - 0.5))!"
+GPFUN_gamma = "gamma(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma_gamma(k))"
+GPFUN__ln_dgamma = "_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x"
+GPFUN_pgamma = "pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)"
+GPFUN_dgamma = "dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))"
+plot [x=63:116] 'images/markov-comparators-16-pct.data' title 'Gemessene Daten', gamma_fit(x) title "Gamma-Verteilung"
+## fit gamma_fit(x) 'images/markov-comparators-16-pct.data' via gamma_k, gamma_theta
+#    EOF

diff --git a/images/markov-comparators-8-pct.data b/images/markov-comparators-8-pct.data
new file mode 100644 (file)
index 0000000..4b8d983
--- /dev/null
+++ b/images/markov-comparators-8-pct.data
@@ -0,0 +1,30 @@
+19 0.534628
+20 1.38496
+21 2.96327
+22 13.6184
+23 22.6531
+24 18.8797
+25 14.8193
+26 9.94546
+27 6.1938
+28 3.8068
+29 2.30663
+30 1.29686
+31 0.702513
+32 0.398067
+33 0.226193
+34 0.122834
+35 0.0688669
+36 0.0349614
+37 0.0206483
+38 0.01138
+39 0.00363692
+40 0.00305032
+41 0.00199444
+42 0.00152516
+43 0.00035196
+44 0.0005866
+45 0.00035196
+46 0
+47 0
+48 0.00011732

diff --git a/images/oe-merge.tex b/images/oe-merge.tex
new file mode 100644 (file)
index 0000000..3cb4146
--- /dev/null
+++ b/images/oe-merge.tex
@@ -0,0 +1,48 @@
+\begin{tikzpicture}[scale=0.80,auto]
+
+% Draw the odd lines
+\foreach \line in {0, 1, 2, 3}
+  \path[edge,rounded corners,color=red]
+       (1+2*\line, 9.0) -- (1+2*\line, 5.5)
+    -- (1+  \line, 4.5) -- (1+  \line, 1.5)
+    -- (1+2*\line, 0.5) -- (1+2*\line,-1.0);
+
+% Draw the even lines
+\foreach \line in {0, 1, 2, 3}
+  \path[edge,rounded corners,color=blue]
+       (2+2*\line, 9.0) -- (2+2*\line, 5.5)
+    -- (5+  \line, 4.5) -- (5+  \line, 1.5)
+    -- (2+2*\line, 0.5) -- (2+2*\line,-1.0);
+
+% Line labels
+\foreach \line in {0, 1, 2, 3}
+  \node at (1+\line,9.3) {$u_\line$};
+\foreach \line in {0, 1, 2, 3}
+  \node at (5+\line,9.3) {$v_\line$};
+\foreach \line in {0, ..., 7}
+  \node at (1+\line,-1.3) {$w_\line$};
+
+% Left sorted list box
+\draw[fill=white] (0.75,6) rectangle (4.25,8);
+\path[gray box] (1,6.25) -- (4,7.75) -- (4,6.25) -- cycle;
+
+% Right sorted list box
+\draw[fill=white] (4.75,6) rectangle (8.25,8);
+\path[gray box] (8,6.25) -- (8,7.75) -- (5,6.25) -- cycle;
+
+% Left OEM block
+\draw[fill=white] (0.75,2) rectangle (4.25,4);
+\node at (2.5,3) {\small $\textrm{OEM}\left(\left\lceil\frac{n}{2}\right\rceil, \left\lceil\frac{m}{2}\right\rceil\right)$};
+
+% Right OEM block
+\draw[fill=white] (4.75,2) rectangle (8.25,4);
+\node at (6.5,3) {\small $\textrm{OEM}\left(\left\lfloor\frac{n}{2}\right\rfloor, \left\lfloor\frac{m}{2}\right\rfloor\right)$};
+
+\foreach \line in {0, 1, 2}
+{
+  \path[comp,very thick] (2+2*\line,0) -- (3+2*\line,0);
+  \draw (2+2*\line,0) circle(5pt)[color=black,fill=black] {};
+  \draw (3+2*\line,0) circle(5pt)[color=black,fill=black] {};
+}
+
+\end{tikzpicture}

diff --git a/images/oe-mergesort-8.tex b/images/oe-mergesort-8.tex
new file mode 100644 (file)
index 0000000..6a8b32b
--- /dev/null
+++ b/images/oe-mergesort-8.tex
@@ -0,0 +1,108 @@
+\begin{tikzpicture}[scale=0.70,auto]
+
+% Box for lower OEM(4)
+\draw[red box] (1,-.333) rectangle (5.35,3.333);
+
+% Box for upper OEM(4)
+\draw[red box] (1,3.667) rectangle (5.35,7.333);
+
+% Box for even merge block
+\draw[blue box] (5.85,-.333) rectangle (7.60,7.333);
+
+% Box for odd merge block
+\draw[blue box] (8.10,-.333) rectangle (9.85,7.333);
+
+% Box for trailing recursive comparators
+\draw[green box] (10.35,-.333) rectangle (11.35,7.333);
+
+\path[edge] (0,0) -- (12.35,0);
+\path[edge] (0,1) -- (12.35,1);
+\path[edge] (0,2) -- (12.35,2);
+\path[edge] (0,3) -- (12.35,3);
+\path[edge] (0,4) -- (12.35,4);
+\path[edge] (0,5) -- (12.35,5);
+\path[edge] (0,6) -- (12.35,6);
+\path[edge] (0,7) -- (12.35,7);
+
+% lower OEM(4)
+\node[vertex] (v0) at (1.50,0) {};
+\node[vertex] (v1) at (1.50,1) {};
+\path[comp] (v0) -- (v1);
+
+\node[vertex] (v2) at (1.50,2) {};
+\node[vertex] (v3) at (1.50,3) {};
+\path[comp] (v2) -- (v3);
+
+\node[vertex] (v8) at (3.00,0) {};
+\node[vertex] (v9) at (3.00,2) {};
+\path[comp] (v8) -- (v9);
+
+\node[vertex] (v10) at (3.35,1) {};
+\node[vertex] (v11) at (3.35,3) {};
+\path[comp] (v10) -- (v11);
+
+\node[vertex] (v16) at (4.85,1) {};
+\node[vertex] (v17) at (4.85,2) {};
+\path[comp] (v16) -- (v17);
+
+% upper OEM(4)
+\node[vertex] (v4) at (1.50,4) {};
+\node[vertex] (v5) at (1.50,5) {};
+\path[comp] (v4) -- (v5);
+
+\node[vertex] (v6) at (1.50,6) {};
+\node[vertex] (v7) at (1.50,7) {};
+\path[comp] (v6) -- (v7);
+
+\node[vertex] (v12) at (3.00,4) {};
+\node[vertex] (v13) at (3.00,6) {};
+\path[comp] (v12) -- (v13);
+
+\node[vertex] (v14) at (3.35,5) {};
+\node[vertex] (v15) at (3.35,7) {};
+\path[comp] (v14) -- (v15);
+
+\node[vertex] (v18) at (4.85,5) {};
+\node[vertex] (v19) at (4.85,6) {};
+\path[comp] (v18) -- (v19);
+
+% Begin of even OE merge (8)
+\node[vertex] (v20) at (6.35,0) {};
+\node[vertex] (v21) at (6.35,4) {};
+\path[comp] (v20) -- (v21);
+
+\node[vertex] (v24) at (6.70,2) {};
+\node[vertex] (v25) at (6.70,6) {};
+\path[comp] (v24) -- (v25);
+
+\node[vertex] (v28) at (7.10,2) {};
+\node[vertex] (v29) at (7.10,4) {};
+\path[comp] (v28) -- (v29);
+
+% Begin of odd OE merge (8)
+\node[vertex] (v22) at (8.60,1) {};
+\node[vertex] (v23) at (8.60,5) {};
+\path[comp] (v22) -- (v23);
+
+\node[vertex] (v26) at (8.95,3) {};
+\node[vertex] (v27) at (8.95,7) {};
+\path[comp] (v26) -- (v27);
+
+\node[vertex] (v30) at (9.35,3) {};
+\node[vertex] (v31) at (9.35,5) {};
+\path[comp] (v30) -- (v31);
+
+% Trailing recursive comparators
+\node[vertex] (v32) at (10.85,1) {};
+\node[vertex] (v33) at (10.85,2) {};
+\path[comp] (v32) -- (v33);
+
+\node[vertex] (v34) at (10.85,3) {};
+\node[vertex] (v35) at (10.85,4) {};
+\path[comp] (v34) -- (v35);
+
+\node[vertex] (v36) at (10.85,5) {};
+\node[vertex] (v37) at (10.85,6) {};
+\path[comp] (v36) -- (v37);
+
+\end{tikzpicture}

diff --git a/images/oe-post-recursive-diff0.tex b/images/oe-post-recursive-diff0.tex
new file mode 100644 (file)
index 0000000..9481f04
--- /dev/null
+++ b/images/oe-post-recursive-diff0.tex
@@ -0,0 +1,50 @@
+\begin{tikzpicture}[scale=0.66,auto]
+
+\pgfmathsetmacro{\lastzeroindex}{0}
+
+% Space between nodes
+\pgfmathsetmacro{\spacingx}{1.3}
+% Amount even boxes are raised
+\pgfmathsetmacro{\offsety}{0.8}
+
+\pgfmathsetmacro{\totalheight}{4 + \offsety} % Height of one sub-picture.
+
+% Lines
+\foreach \x in {0, ..., 7}
+  \draw[edge] (\spacingx * \x, 0) -- (\spacingx * \x, \totalheight);
+
+% Even zero nodes
+\foreach \x in {0, ..., \lastzeroindex}
+{
+  \draw[red box]  (2 * \spacingx * \x - .5, 2 + \offsety) rectangle +(1,1);
+  \draw (2 * \spacingx * \x, 2.5 + \offsety) node {$0$};
+}
+
+% Even one nodes
+\pgfmathsetmacro{\firstoneindex}{\lastzeroindex+1}
+\foreach \x in {\firstoneindex, ..., 3}
+{
+  \draw[blue box] (2 * \spacingx * \x - .5, 2 + \offsety) rectangle +(1,1);
+  \draw (2 * \spacingx * \x, 2.5 + \offsety) node {$1$};
+}
+
+% Odd zero nodes
+\foreach \x in {0, ..., 0}
+{
+  \draw[red box]  (\spacingx + 2 * \spacingx * \x - .5, 2) rectangle +(1,1);
+  \draw (\spacingx + 2 * \spacingx * \x, 2.5) node {$0$};
+}
+
+% Odd one nodes
+\foreach \x in {1, ..., 3}
+{
+  \draw[blue box] (\spacingx + 2 * \spacingx * \x - .5, 2) rectangle +(1,1);
+  \draw (\spacingx + 2 * \spacingx * \x, 2.5) node {$1$};
+}
+
+% Comparators
+\foreach \x in {0, ..., 2}
+  \draw[comp] (    \spacingx + 2 * \spacingx * \x, 1) node[vertex] {}
+           -- (2 * \spacingx + 2 * \spacingx * \x, 1) node[vertex] {};
+
+\end{tikzpicture}

diff --git a/images/oe-post-recursive-diff1.tex b/images/oe-post-recursive-diff1.tex
new file mode 100644 (file)
index 0000000..c2d8e60
--- /dev/null
+++ b/images/oe-post-recursive-diff1.tex
@@ -0,0 +1,50 @@
+\begin{tikzpicture}[scale=0.66,auto]
+
+\pgfmathsetmacro{\lastzeroindex}{1}
+
+% Space between nodes
+\pgfmathsetmacro{\spacingx}{1.3}
+% Amount even boxes are raised
+\pgfmathsetmacro{\offsety}{0.8}
+
+\pgfmathsetmacro{\totalheight}{4 + \offsety} % Height of one sub-picture.
+
+% Lines
+\foreach \x in {0, ..., 7}
+  \draw[edge] (\spacingx * \x, 0) -- (\spacingx * \x, \totalheight);
+
+% Even zero nodes
+\foreach \x in {0, ..., \lastzeroindex}
+{
+  \draw[red box]  (2 * \spacingx * \x - .5, 2 + \offsety) rectangle +(1,1);
+  \draw (2 * \spacingx * \x, 2.5 + \offsety) node {$0$};
+}
+
+% Even one nodes
+\pgfmathsetmacro{\firstoneindex}{\lastzeroindex+1}
+\foreach \x in {\firstoneindex, ..., 3}
+{
+  \draw[blue box] (2 * \spacingx * \x - .5, 2 + \offsety) rectangle +(1,1);
+  \draw (2 * \spacingx * \x, 2.5 + \offsety) node {$1$};
+}
+
+% Odd zero nodes
+\foreach \x in {0, ..., 0}
+{
+  \draw[red box]  (\spacingx + 2 * \spacingx * \x - .5, 2) rectangle +(1,1);
+  \draw (\spacingx + 2 * \spacingx * \x, 2.5) node {$0$};
+}
+
+% Odd one nodes
+\foreach \x in {1, ..., 3}
+{
+  \draw[blue box] (\spacingx + 2 * \spacingx * \x - .5, 2) rectangle +(1,1);
+  \draw (\spacingx + 2 * \spacingx * \x, 2.5) node {$1$};
+}
+
+% Comparators
+\foreach \x in {0, ..., 2}
+  \draw[comp] (    \spacingx + 2 * \spacingx * \x, 1) node[vertex] {}
+           -- (2 * \spacingx + 2 * \spacingx * \x, 1) node[vertex] {};
+
+\end{tikzpicture}