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1、P1:GWO/GQEP2:GWO/GQEQC:FLCCB462-FMSeressJanuary23,200312:11CharCount=0AkosSeress´TheOhioStateUniversityPermutationGroupAlgorithmsiiiP1:GWO/GQEP2:GWO/GQEQC:FLCCB462-FMSeressJanuary23,200312:11CharCount=0publishedbythepresssyndicateoftheuniversityofcambridgeThePittBuilding,TrumpingtonStreet
2、,Cambridge,UnitedKingdomcambridgeuniversitypressTheEdinburghBuilding,CambridgeCB22RU,UK40West20thStreet,NewYork,NY10011-4211,USA477WilliamstownRoad,PortMelbourne,VIC3207,AustraliaRuizdeAlarcon13,28014Madrid,Spain´DockHouse,TheWaterfront,CapeTown8001,SouthAfricahttp://www.cambridge.orgCAk
3、osSeress2003´Thisbookisincopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublished2003PrintedintheUnitedStatesofAmericaTypefaceTimes10/13pt.SystemLA
4、TEX2ε[tb]AcatalogrecordforthisbookisavailablefromtheBritishLibrary.LibraryofCongressCataloginginPublicationDataavailableISBN052166103XhardbackivP1:GWO/GQEP2:GWO/GQEQC:FLCCB462-FMSeressJanuary23,200312:11CharCount=0Contents1Introductionpage11.1AListofAlgorithms41.2NotationandTerminology61.
5、2.1Groups71.2.2PermutationGroups91.2.3AlgorithmicConcepts101.2.4Graphs111.3ClassificationofRandomizedAlgorithms122Black-BoxGroups162.1ClosureAlgorithms182.1.1OrbitComputations182.1.2ClosureofAlgebraicStructures232.2RandomElementsofBlack-BoxGroups242.3RandomSubproducts302.3.1DefinitionandBas
6、icProperties302.3.2ReducingtheNumberofGenerators332.3.3ClosureAlgorithmswithoutMembershipTesting372.3.4DerivedandLowerCentralSeries382.4RandomPrefixes402.4.1DefinitionandBasicProperties402.4.2Applications443PermutationGroups:AComplexityOverview483.1Polynomial-TimeAlgorithms483.2NearlyLinear
7、-TimeAlgorithms513.3Non-Polynomial-TimeMethods52vP1:GWO/GQEP2:GWO/GQEQC:FLCCB462-FMSeressJanuary23,200312:11CharCount=0viContents4BasesandStrongGeneratingSets554.1BasicDefinitions554.2TheSchreier–SimsAlgorithm574.3ThePowerofRandomization624.4ShallowSchreierTrees644.5
