Facets of Combinatorial Optimization: Festschrift for Martin Grötschel PDF
Preview Facets of Combinatorial Optimization: Festschrift for Martin Grötschel
Facets of Combinatorial Optimization Michael Jünger (cid:2) Gerhard Reinelt Editors Facets of Combinatorial Optimization Festschrift for Martin Grötschel Editors MichaelJünger GerhardReinelt Dept.ofComputerScience Dept.ofComputerScience UniversityofCologne UniversityofHeidelberg Cologne,Germany Heidelberg,Germany ISBN978-3-642-38188-1 ISBN978-3-642-38189-8(eBook) DOI10.1007/978-3-642-38189-8 SpringerHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013942544 MathematicsSubjectClassification(2010): 90,90-06,90C ©Springer-VerlagBerlinHeidelberg2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) We dedicatethisbooktoMartinGrötschel on theoccasion ofhis65thbirthday. Preface Wereceivedourdoctoraldegreesintheyears1983and1984;wearetheoldestdoc- toraldescendantsofMartinGrötschelwhocelebratedhis65thbirthdayonSeptem- ber10,2013. Inthesummerof2011,withthishappyoccasionstillmorethantwoyearsinthe future, we wondered what would be a nice birthday present for Martin. We knew thatwewerejustthefirsttwoinalonglistofdoctoraldescendants,butlittledidwe knowthenhowmanytherewere.(Nowwedo,seePartIII.) Wecameupwiththeideaoforganizingacelebrationwithhisdoctoraldescen- dantsandhisclosestscientificfriends.Westartedseriousworkontheprojectdur- ingtheOberwolfachWorkshoponCombinatorialOptimizationinNovember2011, where we also decided to organize a colloquium in his honor at the University of CologneonSeptember13,2013,andtoeditthisbookthatwillbepresentedtohim andallparticipantsduringthecolloquium. Many of Martin Grötschel’s doctoral descendants still work in research, in and outsideacademia.WhenweissuedacallforcontributionsonNovember24,2011, includingthesentence“Weaimatthehighestquality,sopleasededicateyourbest workinhonorofMartinGrötschel!”,wehadanoverwhelminglypositiveresponse. The result is Part IV, the core of this book.It is preceded by a personal tribute by the editors to our mentor (Part I), a contribution by a very special “predecessor” (PartII),andthedoctoraldescendanttree1983–2012(PartIII). Cologne,Germany MichaelJünger Heidelberg,Germany GerhardReinelt September2013 vii Acknowledgements Preparing this book and organizing the Festkolloquium have been intertwined tasks that turnedouttobemuchmoredemandingthanwehadanticipatedwhenwesketchedtheideas abouttwoyearsago.Manypeoplehelpedus.Wewouldliketoexpressourgratitudeto • IrisGrötschelforadvice,photos,andforkeepingthesecret, • BernhardKorteforvaluableinformationontheearlydaysattheInstitutfürÖkonometrie undOperationsResearchoftheUniversityofBonn, • DirkjeKeiperandSimonaSchöneweißforexploringthearchivesoftheForschungsinstitut fürDiskreteMathematikattheUniversityofBonnforus, • TeodoraUngureanuforhelpingusrefreshourmemoriesofthedaysattheMathematics DepartmentoftheUniversityofAugsburg, • Uwe and Renate Zimmermann for turning scans of blurred photographs into reasonable pictures, • BillPulleyblankforreadingapreliminaryversionofthefirstchapterandprovidingvery helpfulfeedback, • ManfredPadbergforcontinuous“grandparental”advicebeforeandduringthepreparation ofthisbookandhisimmediateagreementtocontributehislatestarticletothisbook, • SvenMallachforhishelpintypesettingManfredPadberg’scontribution, • thedoctoraldescendantswhohelpedgettingthedoctoraldescendanttreeright, • ThomasMöllmannwhodidnothesitatewhenweapproachedhimwiththedemandingtask ofturningamathematician’streeintoarealtree, • theauthorsofPartIIandPartIV,whopatientlydealtwithourmanyrequestsandstrict deadlines, • theanonymousrefereeswhosupporteduswiththeirexpertknowledgeandgavevaluable advicetotheauthors, • MartinPetersofSpringerVerlagwhosupportedthisbookprojectfromtheverybeginning, • RuthAlleweltofSpringerVerlagwhoaccompaniedusallthewayfromtheearlystagesto thefinalbook, • FrankHolzwarthofSpringerVerlagwhoprovided“quickLATEXhacks”wheneverneeded inthetechnicalediting, • GöntjeTeuchertforcoordinatingtheorganizationoftheFestkolloquium,and • MartinGronemann,ThomasLange,SvenMallach,DanielSchmidt,andChristianeSpisla forproofreadingthebookandfortheirhelpintheorganizationoftheFestkolloquium. ix Contents PartI MartinGrötschel—ActivistinOptimization MartinGrötschel—TheEarlyYearsinBonnandAugsburg . . . . . . . . 5 MichaelJüngerandGerhardReinelt 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Bonn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Augsburg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Part II Contribution by a Very Special Predecessor of Martin Grötschel FacetsandRankofIntegerPolyhedra . . . . . . . . . . . . . . . . . . . . 23 ManfredW.Padberg 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2 NormalFormandClassificationofFacets. . . . . . . . . . . . . . 26 3 IrreducibleRepresentationsofFacets . . . . . . . . . . . . . . . . 30 4 SymmetryofVertexFigures . . . . . . . . . . . . . . . . . . . . . 31 5 SymmetryofEdgeFigures . . . . . . . . . . . . . . . . . . . . . 35 6 RankofFacetsandIntegerPolyhedra . . . . . . . . . . . . . . . . 37 7 TheFacialStructureof“Small”STSPolytopes . . . . . . . . . . . 45 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 PartIII MartinGrötschel’sDoctoralDescendants MartinGrötschel’sDescendantsandTheirDoctoralTheses1983–2012 . 63 MichaelJüngerandGerhardReinelt PartIV ContributionsbyMartinGrötschel’sDoctoralDescendants ConstructingExtendedFormulationsfromReflectionRelations . . . . . 77 VolkerKaibelandKanstantsinPashkovich 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 xi xii Contents 2 PolyhedralRelations . . . . . . . . . . . . . . . . . . . . . . . . . 80 3 ReflectionRelations . . . . . . . . . . . . . . . . . . . . . . . . . 87 4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.1 ReflectionGroups . . . . . . . . . . . . . . . . . . . . . . 89 4.2 HuffmanPolytopes . . . . . . . . . . . . . . . . . . . . . 94 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Mirror-DescentMethodsinMixed-IntegerConvexOptimization . . . . . 101 MichelBaes,TimmOertel,ChristianWagner,andRobertWeismantel 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 2 AnAlgorithmBasedonan“ImprovementOracle” . . . . . . . . . 103 3 Two-DimensionalIntegerConvexOptimization . . . . . . . . . . 109 3.1 MinimizingaConvexFunctioninTwoIntegerVariables . . 110 3.2 Findingthek-thBestPoint . . . . . . . . . . . . . . . . . 114 4 ExtensionsandApplicationstotheGeneralSetting . . . . . . . . . 120 4.1 Mixed-IntegerConvexProblemswithOneIntegerVariable 121 4.2 Mixed-IntegerConvexProblemswithTwoIntegerVariables 127 4.3 A Finite-Time Algorithm for Mixed-Integer Convex Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 129 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 BeyondPerfection:ComputationalResultsforSuperclasses . . . . . . . . 133 ArnaudPêcherandAnnegretK.Wagler 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 2 BeyondPerfection . . . . . . . . . . . . . . . . . . . . . . . . . . 138 2.1 OnComputingtheCliqueNumber . . . . . . . . . . . . . 141 2.2 OnComputingtheChromaticNumber . . . . . . . . . . . 146 2.3 OnComputingtheCircular-CliqueandCircular-Chromatic Number . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 3 ExtendingtheThetaFunctiontoLargerConvexSetsofMatrices . 156 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 FromVertex-TelecenterstoSubtree-Telecenters . . . . . . . . . . . . . . 163 ZawWinandChoKyiThan 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 2 Vertex-CentroidsandVertex-TelecentersofaTree . . . . . . . . . 164 3 Subtree-CentroidsandSubtree-TelecentersofaTree . . . . . . . . 166 4 ACharacterizationofSubtree-Telecenters . . . . . . . . . . . . . 168 5 RelationBetweenSubtree-CentroidsandSubtree-Telecenters . . . 171 5.1 ASolutionMethodforFindingaSubtree-Telecenterofa GivenTree . . . . . . . . . . . . . . . . . . . . . . . . . . 172 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Contents xiii AlgorithmsforJunctionsinAcyclicDigraphs . . . . . . . . . . . . . . . . 175 CarlosEduardoFerreiraandÁlvaroJunioPereiraFranco 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 2 ConceptsandNotation . . . . . . . . . . . . . . . . . . . . . . . . 176 3 ProblemDefinition,LiteratureOverview,andMainResults . . . . 178 4 PolynomialTimeAlgorithmsforthes-Junction-k-PairsProblem . 179 5 AnO(m+k)TimeAlgorithmforthes-Junction-k-PairsProblem 180 6 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 7 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 AlgorithmsforSchedulingSensorstoMaximizeCoverageTime . . . . . 195 RafaeldaPonteBarbosaandYoshikoWakabayashi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 2 TheProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 3 TheApproximationAlgorithmforRSCandItsAnalysis . . . . . . 199 3.1 ApproximationRatiooftheAlgorithm . . . . . . . . . . . 199 4 ILPFormulationfortheRSCProblemandComputationalResults . 208 5 TheRSCPProblem,thePreemptiveVariant . . . . . . . . . . . . 210 6 ConcludingRemarks. . . . . . . . . . . . . . . . . . . . . . . . . 213 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 HowManySteinerTerminalsCanYouConnectin20Years? . . . . . . . 215 RalfBorndörfer,Nam-Du˜ngHoang,MarikaKarbstein,ThorstenKoch, andAlexanderMartin 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 2 TheSteinerConnectivityProblem . . . . . . . . . . . . . . . . . . 216 2.1 TheAll-TerminalCaseandtheGreedyAlgorithm . . . . . 217 2.2 The2-TerminalCaseandtheCompanionTheoremto Menger’sTheorem . . . . . . . . . . . . . . . . . . . . . . 224 3 TheSteinerTreePackingProblem . . . . . . . . . . . . . . . . . 228 3.1 ValidInequalities . . . . . . . . . . . . . . . . . . . . . . 231 3.2 Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . . 233 3.3 ComputationalResults . . . . . . . . . . . . . . . . . . . . 236 4 ConclusionandOutlook . . . . . . . . . . . . . . . . . . . . . . . 242 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 TheMaximumWeightConnectedSubgraphProblem . . . . . . . . . . . 245 EduardoÁlvarez-Miranda,IvanaLjubic´,andPetraMutzel 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 2 TheMaximumWeightConnectedSubgraphProblem . . . . . . . 247 3 MIPFormulationsfortheMWCS . . . . . . . . . . . . . . . . . . 249 3.1 ThePrize-CollectingSteinerTreeModel . . . . . . . . . . 249 3.2 ModelofBackesetal.2011 . . . . . . . . . . . . . . . . . 251 3.3 AModelBasedon(k,(cid:2))Node-Separators . . . . . . . . . 252
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