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\contentsline {section}{\textbf {Teil A -- Die Grundlagen}}{5}{part*.2}%
\contentsline {section}{\numberline {1}Der Ausgangspunkt: ein widerspenstiges Problem}{5}{section.1}%
\contentsline {section}{\numberline {2}Die Klasse P: was \quotedblbase schnell\textquotedblleft {} heißen soll}{6}{section.2}%
\contentsline {section}{\numberline {3}Die Klasse NP: Lösungen prüfen statt finden}{7}{section.3}%
\contentsline {subsection}{\numberline {3.1}Zertifikate und Verifizierer}{7}{subsection.3.1}%
\contentsline {subsection}{\numberline {3.2}Dieselbe Klasse über das Raten}{7}{subsection.3.2}%
\contentsline {subsection}{\numberline {3.3}Das Verhältnis von P und NP}{8}{subsection.3.3}%
\contentsline {section}{\numberline {4}Reduktionen: das Vergleichswerkzeug}{8}{section.4}%
\contentsline {section}{\numberline {5}NP-Vollständigkeit: die härtesten Probleme in NP}{9}{section.5}%
\contentsline {subsection}{\numberline {5.1}Cook--Levin: das erste harte Problem}{10}{subsection.5.1}%
\contentsline {subsection}{\numberline {5.2}Der Dominoeffekt}{10}{subsection.5.2}%
\contentsline {section}{\textbf {Teil B -- Der Katalog aller Probleme}}{11}{part*.3}%
\contentsline {section}{\numberline {6}SAT}{11}{section.6}%
\contentsline {section}{\numberline {7}3-SAT}{13}{section.7}%
\contentsline {section}{\numberline {8}$k$-Clique}{15}{section.8}%
\contentsline {section}{\numberline {9}Independent Set}{17}{section.9}%
\contentsline {section}{\numberline {10}Vertex Cover}{18}{section.10}%
\contentsline {section}{\numberline {11}Feedback Vertex Set}{20}{section.11}%
\contentsline {section}{\numberline {12}$\Delta $-Cover}{21}{section.12}%
\contentsline {section}{\numberline {13}$k$-Color}{23}{section.13}%
\contentsline {section}{\numberline {14}Hamiltonkreis}{24}{section.14}%
\contentsline {section}{\numberline {15}TSP}{26}{section.15}%
\contentsline {section}{\numberline {16}3-dimensionales Matching}{27}{section.16}%
\contentsline {section}{\numberline {17}3-Exact Cover}{28}{section.17}%
\contentsline {section}{\numberline {18}SubSet Sum}{29}{section.18}%
\contentsline {section}{\numberline {19}Partition}{32}{section.19}%
\contentsline {section}{\numberline {20}Knapsack}{33}{section.20}%
\contentsline {section}{\numberline {21}$P\|C_{\max }$ (Scheduling)}{34}{section.21}%
\contentsline {section}{\numberline {22}Hitting Set}{35}{section.22}%
\contentsline {section}{\numberline {23}Set Cover}{36}{section.23}%
\contentsline {section}{\numberline {24}Dominating Set}{38}{section.24}%
\contentsline {section}{\numberline {25}Longest Path}{39}{section.25}%
\contentsline {section}{\numberline {26}Das Halteproblem}{39}{section.26}%
\contentsline {section}{\textbf {Teil C -- Untere Schranken mit der ETH}}{40}{part*.64}%
\contentsline {section}{\numberline {27}Das Handwerkszeug}{41}{section.27}%
\contentsline {section}{\numberline {28}Die Schranken im Einzelnen}{42}{section.28}%
\contentsline {section}{\textbf {Teil D -- Approximation}}{44}{part*.76}%
\contentsline {section}{\numberline {29}Was eine Güte-Garantie ist}{44}{section.29}%
\contentsline {section}{\numberline {30}TSP ohne Zusatzannahme: hoffnungslos}{45}{section.30}%
\contentsline {section}{\numberline {31}$\Delta $TSP$_1$: Gerüst, Rundweg, Abkürzung}{45}{section.31}%
\contentsline {section}{\numberline {32}Christofides: das Matching statt der Verdopplung}{47}{section.32}%
\contentsline {section}{\numberline {33}Knapsack, Stufe 1: der pure Greedy}{48}{section.33}%
\contentsline {section}{\numberline {34}Knapsack, Stufe 2: Modified Greedy}{49}{section.34}%
\contentsline {section}{\numberline {35}Knapsack, Stufe 3: Sahni-Schema}{49}{section.35}%
\contentsline {section}{\numberline {36}Knapsack, Stufe 4: das FPTAS}{50}{section.36}%
\contentsline {section}{\numberline {37}Scheduling, Regel 1: List Scheduling}{50}{section.37}%
\contentsline {section}{\numberline {38}Scheduling, Regel 2: LPT}{51}{section.38}%
\contentsline {section}{\numberline {39}Parallel-Task-Scheduling: Jobs, die mehrere Maschinen brauchen}{51}{section.39}%
\contentsline {section}{\numberline {40}Strip Packing: der NFDH-Algorithmus}{52}{section.40}%
\contentsline {section}{\numberline {41}MAX-3-SAT: zwei Versuche reichen für Güte 2}{54}{section.41}%
\contentsline {section}{\numberline {42}Vertex Cover: die Beide-Endpunkte-Regel}{55}{section.42}%
\contentsline {section}{\numberline {43}Schlusswort}{55}{section.43}%