Computational Complexity: Theory, Techniques, and Applications

3532 Pages·2012·96.373 MB·English

by  Burton Voorhees (auth.), Robert A. Meyers Ph. D. (eds.)

ComputationalComplexity
Theory,Techniques,andApplications
Thisbookconsistsofselectionsfromthe
EncyclopediaofComplexityandSystemsScience
editedbyRobertA.Meyers,
publishedbySpringerNewYorkin2009.
Robert A. Meyers (Ed.)
Computational Complexity
Theory, Techniques, and Applications
With1487Figuresand234Tables
123
ROBERTA.MEYERS,Ph.D.
Editor-in-Chief
RAMTECHLIMITED
122EscalleLane
Larkspur,CA94939
USA
[e-mail]
LibraryofCongressControlNumber:2011940800
ISBN:978-1-4614-1800-9
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PrintandelectronicbundleunderISBN978-1-4614-1801-6
©2012SpringerScience+BusinessMedia,LLC.
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tifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietary
rights.
ThisbookconsistsofselectionsfromtheEncyclopediaofComplexityandSystemsScienceeditedbyRobertA.Meyers,
publishedbySpringerNewYorkin2009.
springer.com
Printedonacidfreepaper
Preface
Complexsystemsaresystemsthatcomprisemanyinteractingpartswiththeabilitytogenerateanewqualityofcollective
behaviorthroughself-organization,e.g.thespontaneousformationoftemporal,spatialorfunctionalstructures.They
aretherefore adaptiveas theyevolveand maycontain self-driving feedbackloops. Thus, complexsystemsare much
morethanasumoftheirparts.Complexsystemsareoftencharacterizedashavingextremesensitivitytoinitialcondi-
tionsaswellasemergentbehaviorthatarenotreadilypredictableorevencompletelydeterministic.Theconclusionis
thatareductionist(bottom-up)approachisoftenanincompletedescriptionofaphenomenon.Thisrecognition,that
thecollectivebehaviorofthewholesystemcannotbesimplyinferredfromtheunderstandingofthebehaviorofthein-
dividualcomponents,hasledtomanynewconceptsandsophisticatedmathematicalandmodelingtoolsforapplication
tomanyscientific, engineering,andsocietalissuesthatcanbeadequatelydescribedonlyintermsofcomplexityand
complexsystems.
Theinherentdifficulty, orhardness,ofcomputational problemsincomplexsystemsis afundamentalconcept in
computational complexitytheory.Thiscompendium,ComputationalComplexity, presentsadetailedintegratedview
ofthetheoreticalbasis,computationalmethodsandnewestapplicableapproachestosolvinginherentlydifficultprob-
lemswhosesolutionrequiresextensiveresourcesapproachingthepracticallimitsofpresentdaycomputersystems.Key
componentsofcomputationalcomplexityaredetailed,integratedandutilized,varyingfromParameterizedComplexity
Theory(e.g.seearticlesentitled(cid:2)QuantumComputing,and(cid:2)AnalogComputation),theExponentialTimeHypoth-
esis(e.g.seearticleson(cid:2)CellularAutomataandLanguageTheory)andComplexityClassP(e.g.see(cid:2)QuantumCom-
putationalComplexityand(cid:2)CellularAutomata,Universalityof),toHeuristics(e.g.(cid:2)SocialNetworkVisualization,
Methodsofand(cid:2)RepeatedGameswithIncompleteInformation)andParallelAlgorithms(e.g.(cid:2)CellularAutomata
asModelsofParallelComputationand(cid:2)OpticalComputing).
Thereare209articleswhichhavebeenorganizedinto14sectionseachheadedbyarecognizedexpertinthefield
andsupportedbypeerreviewersinadditiontothesectioneditor.Thesectionsare:
(cid:2) AgentBasedModelingandSimulation
(cid:2) CellularAutomata,MathematicalBasisof
(cid:2) ComplexNetworksandGraphTheory
(cid:2) DataMiningandKnowledgeDiscovery
(cid:2) GameTheory
(cid:2) GranularComputing
(cid:2) IntelligentSystems
(cid:2) ProbabilityandStatisticsinComplexSystems
(cid:2) QuantumInformationScience
(cid:2) SocialNetworkAnalysis
(cid:2) SocialScience,PhysicsandMathematics,Applicationsin
(cid:2) SoftComputing
(cid:2) UnconventionalComputing
(cid:2) Wavelets
ThecompletelistingofarticlesandsectioneditorsispresentedonpagesVIItoXII.
VI Preface
Thearticlesarewrittenforanaudienceofadvanceduniversityundergraduateandgraduatestudents,professors,and
professionalsinawiderangeoffieldswhomustmanagecomplexityonscalesrangingfromtheatomicandmolecular
tothesocietalandglobal.Eacharticlewasselectedandpeerreviewedbyoneofour13SectionEditorswithadviceand
consultationprovidedbyBoardMembers:LotfiZadeh,StephenWolframandRichardStearns,andtheEditor-in-Chief.
Thislevelofcoordinationassuresthatthereadercanhavealevelofconfidenceintherelevanceandaccuracyofthe
information farexceeding thatgenerallyfound on the World Wide Web.Accessibility is alsoa priority and for this
reasoneacharticleincludesaglossaryofimportanttermsandaconcisedefinitionofthesubject.
RobertA.Meyers
Editor-in-Chief
Larkspur,California
July2011
Sections
AgentBasedModelingandSimulation,
SectionEditor:FilippoCastiglione
AgentBasedComputationalEconomics
AgentBasedModelingandArtificialLife
AgentBasedModelingandComputerLanguages
AgentBasedModelingandSimulation,Introductionto
AgentBasedModeling,LargeScaleSimulations
AgentBasedModeling,MathematicalFormalismfor
Agent-BasedModelingandSimulation
CellularAutomatonModelingofTumorInvasion
ComputerGraphicsandGames,AgentBasedModelingin
EmbodiedandSituatedAgents,AdaptiveBehaviorin
InteractionBasedComputinginPhysics
LogicandGeometryofAgentsinAgent-BasedModeling
SocialPhenomenaSimulation
SwarmIntelligence
CellularAutomata,MathematicalBasisof,
SectionEditor:AndrewAdamatzky
AdditiveCellularAutomata
AlgorithmicComplexityandCellularAutomata
CellularAutomataandGroups
CellularAutomataandLanguageTheory
CellularAutomataasModelsofParallelComputation
CellularAutomatainHyperbolicSpaces
CellularAutomataModelingofPhysicalSystems
CellularAutomataonTriangular,PentagonalandHexagonalTessellations
CellularAutomatawithMemory
CellularAutomata,Classificationof
CellularAutomata,EmergentPhenomenain
CellularAutomata,Universalityof
ChaoticBehaviorofCellularAutomata
DynamicsofCellularAutomatainNon-compactSpaces
ErgodicTheoryofCellularAutomata
EvolvingCellularAutomata
FiringSquadSynchronizationProbleminCellularAutomata
GlidersinCellularAutomata
GrowthPhenomenainCellularAutomata
IdentificationofCellularAutomata
MathematicalBasisofCellularAutomata,Introductionto
VIII Sections
PhaseTransitionsinCellularAutomata
QuantumCellularAutomata
ReversibleCellularAutomata
Self-organisedCriticalityandCellularAutomata
Self-ReplicationandCellularAutomata
StructurallyDynamicCellularAutomata
TilingProblemandUndecidabilityinCellularAutomata
TopologicalDynamicsofCellularAutomata
ComplexNetworksandGraphTheory,
SectionEditor:GeoffreyCanright
CommunityStructureinGraphs
ComplexGeneRegulatoryNetworks–FromStructuretoBiologicalObservables:CellFateDetermination
ComplexNetworksandGraphTheory
ComplexNetworks,Visualizationof
FoodWebs
GrowthModelsforNetworks
HumanSexualNetworks
InternetTopology
LinkAnalysisandWebSearch
MotifsinGraphs
Non-negativeMatricesandDigraphs
RandomGraphs,aWhirlwindTourof
SynchronizationPhenomenaonNetworks
WorldWideWeb,GraphStructure
DataMiningandKnowledgeDiscovery,
SectionEditor:PeterKokol
DataandDimensionalityReductioninDataAnalysisandSystemModeling
Data-MiningandKnowledgeDiscovery,Introductionto
Data-MiningandKnowledgeDiscovery,NeuralNetworksin
Data-MiningandKnowledgeDiscovery:CaseBasedReasoning,NearestNeighborandRoughSets
DecisionTrees
DiscoverySystems
GeneticandEvolutionaryAlgorithmsandProgramming:GeneralIntroductionandApplicationtoGamePlaying
KnowledgeDiscovery:Clustering
MachineLearning,EnsembleMethodsin
ManipulatingDataandDimensionReductionMethods:FeatureSelection
GameTheory,
SectionEditor:MarildaSotomayor
BayesianGames:GameswithIncompleteInformation
CooperativeGames
CooperativeGames(VonNeumann–MorgensternStableSets)
CorrelatedEquilibriaandCommunicationinGames
CostSharing
DifferentialGames
DynamicGameswithanApplicationtoClimateChangeModels
EvolutionaryGameTheory
FairDivision
Sections IX
GameTheoryandStrategicComplexity
GameTheory,Introductionto
ImplementationTheory
InspectionGames
LearninginGames
MarketGamesandClubs
MechanismDesign
NetworksandStability
Principal-AgentModels
RepeatedGameswithCompleteInformation
RepeatedGameswithIncompleteInformation
ReputationEffects
SignalingGames
StaticGames
StochasticGames
Two-SidedMatchingModels
Voting
VotingProcedures,Complexityof
Zero-sumTwoPersonGames
GranularComputing,
SectionEditor:TsauY.Lin
CooperativeMulti-HierarchicalQueryAnsweringSystems
DependencyandGranularityinDataMining
FuzzyLogic
FuzzyProbabilityTheory
FuzzySystemModelsEvolutionfromFuzzyRulebasestoFuzzyFunctions
Genetic-FuzzyDataMiningTechniques
GranularModelforDataMining
GranularComputingandDataMiningforOrderedData:TheDominance-BasedRoughSetApproach
GranularComputingandModelingoftheUncertaintyinQuantumMechanics
GranularComputingSystemVulnerabilities:ExploringtheDarkSideofSocialNetworkingCommunities
GranularComputing,InformationModelsfor
GranularComputing,Introductionto
GranularComputing,PhilosophicalFoundationfor
GranularComputing,PrinciplesandPerspectivesof
GranularComputing:Practices,TheoriesandFutureDirections
GranularNeuralNetwork
GranulationofKnowledge:SimilarityBasedApproachinInformationandDecisionSystems
Multi-GranularComputingandQuotientStructure
Non-standardAnalysis,anInvitationto
RoughandRough-FuzzySetsinDesignofInformationSystems
RoughSetDataAnalysis
RuleInduction,MissingAttributeValuesandDiscretization
SocialNetworksandGranularComputing
IntelligentSystems,
SectionEditor:JamesA.Hendler
ArtificialIntelligenceinModelingandSimulation
IntelligentControl
IntelligentSystems,Introductionto
X Sections
LearningandPlanning(IntelligentSystems)
MobileAgents
SemanticWeb
ProbabilityandStatisticsinComplexSystems,
SectionEditor:HenrikJeldtoftJensen
BayesianStatistics
BranchingProcesses
ComplexityinSystemsLevelBiologyandGenetics:StatisticalPerspectives
CorrelationsinComplexSystems
Entropy
ExtremeValueStatistics
FieldTheoreticMethods
Fluctuations,Importanceof:ComplexityintheViewofStochasticProcesses
HierarchicalDynamics
LevyStatisticsandAnomalousTransport:LevyFlightsandSubdiffusion
ProbabilityandStatisticsinComplexSystems,Introductionto
ProbabilityDensitiesinComplexSystems,Measuring
ProbabilityDistributionsinComplexSystems
RandomMatrixTheory
RandomWalksinRandomEnvironment
RecordStatisticsandDynamics
StochasticLoewnerEvolution:LinkingUniversality,CriticalityandConformalInvarianceinComplexSystems
StochasticProcesses
QuantumInformationScience,
SectionEditor:JosephF.Traub
QuantumAlgorithms
QuantumAlgorithmsandComplexityforContinuousProblems
QuantumComputationalComplexity
QuantumComputingUsingOptics
QuantumComputingwithTrappedIons
QuantumCryptography
QuantumErrorCorrectionandFaultTolerantQuantumComputing
QuantumInformationProcessing
QuantumInformationScience,Introductionto
SocialNetworkAnalysis,
SectionEditor:JohnScott
NetworkAnalysis,LongitudinalMethodsof
PositionalAnalysisandBlockmodelling
SocialNetworkAnalysis,EstimationandSamplingin
SocialNetworkAnalysis,GraphTheoreticalApproachesto
SocialNetworkAnalysis,Large-Scale
SocialNetworkAnalysis,Overviewof
SocialNetworkAnalysis,Two-ModeConceptsin
SocialNetworkVisualization,Methodsof
SocialNetworks,AlgebraicModelsfor
SocialNetworks,DiffusionProcessesin
SocialNetworks,ExponentialRandomGraph(p*)Modelsfor