From: Martin Mares Date: Thu, 25 Jan 2007 12:50:14 +0000 (+0100) Subject: Hezci obrazek rezu. X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=21457702da7e51b1870023754359ac40a443c9b5;p=ga.git Hezci obrazek rezu. --- diff --git a/2-dinic/2-dinic.tex b/2-dinic/2-dinic.tex index 7a19ca5..d4189b0 100644 --- a/2-dinic/2-dinic.tex +++ b/2-dinic/2-dinic.tex @@ -162,6 +162,10 @@ odhad na~po Tím jsme dokázali, ¾e celková slo¾itost Dinicova algoritmu pro jednotkové kapacity je $\O(m^{3/2})$. Tím jsme si pomohli pro øídké grafy. +\vbox{ +\vbox to 0pt{\vskip 2ex\rightline{\epsfxsize=0.2\hsize\epsfbox{dinic-vrcholrez.eps}}\vss}\vskip-\baselineskip +\hangindent=-0.25\hsize +\hangafter=-10 \s{Jednotkové kapacity a jeden ze stupòù roven 1:} Úlohu hledání maximálního párování v~bipartitním grafu, pøípadnì hledání vrcholovì disjunktních cest v~obecném grafu lze pøevést (viz pøedchozí kapitola) @@ -169,10 +173,10 @@ na~hled nebo výstupní stupeò roven jedné. Pro takovou sí» mù¾eme pøedchozí odhad je¹tì tro¹ku upravit. Pokusíme se nalézt v síti po~$k$~krocích nìjaký malý øez. Místo rozhraní budeme hledat jednu malou -vrstvu a z malé vrstvy vytvoøíme malý øez tak, ¾e pro ka¾dý vrchol z vrstvy vezmeme tu hranu, +vrstvu a z~malé vrstvy vytvoøíme malý øez tak, ¾e pro ka¾dý vrchol z~vrstvy vezmeme tu hranu, která je ve svém smìru sama. -\figure{dinic-vrcholrez.eps}{Øez podle vrcholù ve vrstvì}{0.2\hsize} +} Po $k$ krocích máme alespoò $k$ vrstev, a~proto existuje vrstva $\delta$ s nejvý¹e $n/k$ vrcholy. Tedy existuje øez $C$ o~velikosti $\vert C\vert \leq n/k$ (získáme z vrstvy $\delta$ vý¹e popsaným postupem). diff --git a/2-dinic/dinic-vrcholrez.eps b/2-dinic/dinic-vrcholrez.eps index a0d5bee..aca8b98 100644 --- a/2-dinic/dinic-vrcholrez.eps +++ b/2-dinic/dinic-vrcholrez.eps @@ -1,11 +1,11 @@ %!PS-Adobe-2.0 EPSF-2.0 -%%Title: Diagram2.dia +%%Title: Diagram1.dia %%Creator: Dia v0.94 -%%CreationDate: Tue Jan 23 17:57:45 2007 +%%CreationDate: Thu Jan 25 13:23:41 2007 %%For: mares %%Orientation: Portrait %%Magnification: 1.0000 -%%BoundingBox: 0 0 196 210 +%%BoundingBox: 0 0 195 210 %%BeginSetup %%EndSetup %%EndComments @@ -123,100 +123,100 @@ putinterval 1.000000 1.000000 1.000000 srgb -n 5.392537 5.700000 0.950000 3.650000 0 360 ellipse f +n 5.363000 5.700000 0.950000 3.650000 0 360 ellipse f 0.100000 slw [] 0 sd [] 0 sd 0.000000 0.000000 0.000000 srgb -n 5.392537 5.700000 0.950000 3.650000 0 360 ellipse cp s +n 5.363000 5.700000 0.950000 3.650000 0 360 ellipse cp s 0.100000 slw -[] 0 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