From 21457702da7e51b1870023754359ac40a443c9b5 Mon Sep 17 00:00:00 2001 From: Martin Mares Date: Thu, 25 Jan 2007 13:50:14 +0100 Subject: [PATCH] Hezci obrazek rezu. --- 2-dinic/2-dinic.tex | 8 ++- 2-dinic/dinic-vrcholrez.eps | 94 ++++++++++++++++++------------------ 2-dinic/dinic.dia | Bin 11036 -> 11028 bytes 3 files changed, 53 insertions(+), 49 deletions(-) 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. 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