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Lecture 4

Week 4 - Cliques and 3SAT, Proof by Induction.pdf

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Department
Computer Science
Course
CSCA67H3
Professor
Anna Bretscher
Semester
Fall

Description
CliquesinGraphsDenitionAcliqueinagraphisasetSofverticessuchthateverypairofverticesinSareadjacentIfthecliquehasnverticesitisdenotedbyKnK5FindingmaximalsizedcliquesinlargegraphsisachallengingproblemindataminingieanalyzingdataclusteringMaximalcliquedetectionarisesinbioinformaticsanalysisofsocialnetworkingpatternswebpageclusteringetcCliquesand3SATRecall3SATGivenasetofclausesCfCCCgeachofsize12k3overasetofvariablesXfxxxgdoestheren12existatruthassignmentthatsatisesC13SATandCliquesSupposewehavea3SATformulaFaORbORdANDbORcORdANDaORcORdANDaORbORcConsiderthefollowingalgorithmtoconstructagraphfromF1CreateavertexforeachliteralintheformulaUsetheliteraltolabelthevertex2Grouptheverticescorrespondingtoaclausetogether3ConnecttwoverticesinthegraphiftheyareIndifferentclausesandarenotanegationofeachotherExamplebadabbcdccad2
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