Facets of Combinatorial Optimization: Festschrift for Martin Grötschel

510 Pages·2013·7.696 MB·English

by  Michael Jünger, Gerhard Reinelt (auth.), Michael Jünger, Gerhard Reinelt (eds.)

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
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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