Graph Algorithms

204 Pages·2011·1.47 MB·English

by  Shimon Even

GraphAlgorithms,2ndEdition
ShimonEven’sGraphAlgorithms,publishedin1979,wasaseminalintroductorybook
onalgorithmsreadbyeveryone engaged inthefield.Thisthoroughly revisedsecond
edition,withaforewordbyRichardM.KarpandnotesbyAndrewV.Goldberg,continues
theexceptionalpresentationfromthefirsteditionandexplainsalgorithmsinformalbut
simplelanguagewithadirectandintuitivepresentation.
Thematerialcoveredbythebookbeginswithbasicmaterial,includinggraphsand
shortestpaths,trees,depth-firstsearch,andbreadth-firstsearch. Themainpartof the
bookisdevotedtonetworkflowsandapplicationsofnetworkflows.Thebookendswith
twochaptersonplanargraphsandontestinggraphplanarity.
SHIMON EVEN (1935–2004) wasapioneeringresearcherongraphalgorithmsand
cryptography.Hewasahighlyinfluentialeducatorwhoplayedamajorroleinestablish-
ingcomputerscienceeducationinIsraelattheWeizmannInstituteandtheTechnion.
Heservedasasourceofprofessional inspirationandasarolemodelforgenerations
ofstudentsandresearchers.HeistheauthorofAlgorithmicCombinatorics(1973)and
GraphAlgorithms(1979).

Graph Algorithms
2ndEdition
SHIMON EVEN
Editedby
GUY EVEN
Tel-AvivUniversity
CAMBRIDGE UNIVERSITY PRESS
Cambridge,NewYork,Melbourne,Madrid,CapeTown,
Singapore,SãoPaulo,Delhi,Tokyo,MexicoCity
CambridgeUniversityPress
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521736534
©ShimonEven1979
©ShimonEvenandGuyEven2012
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firsteditionpublished1979byComputerSciencePress
Secondeditionpublished2012
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationData
ISBN978-0-521-51718-8Hardback
ISBN978-0-521-73653-4Paperback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofURLs
for external or third-party Internet Web sites referred to in this publication and does not
guarantee that any content on such Web sites is, or will remain, accurate or appropriate.
Contents
ForewordbyRichardM.Karp pagevii
PrefacetotheSecondEdition ix
PrefacetotheFirstEdition xi
1 PathsinGraphs 1
1.1 IntroductiontoGraphTheory 1
1.2 ComputerRepresentationofGraphs 3
1.3 EulerGraphs 6
1.4 DeBruijnSequences 9
1.5 Shortest-PathAlgorithms 11
1.6 Problems 22
2 Trees 29
2.1 TreeDefinitions 29
2.2 MinimumSpanningTree 31
2.3 Cayley’sTheorem 34
2.4 DirectedTreeDefinitions 37
2.5 TheInfinityLemma 39
2.6 Problems 42
3 Depth-FirstSearch 46
3.1 DFSofUndirectedGraphs 46
3.2 AlgorithmforNonseparableComponents 52
3.3 DFSonDirectedGraphs 57
3.4 StronglyConnectedComponentsofaDigraph 58
3.5 Problems 62
4 OrderedTrees 65
4.1 UniquelyDecipherableCodes 65
v
vi Contents
4.2 PositionalTreesandHuffman’sOptimizationProblem 69
4.3 ApplicationoftheHuffmanTreetoSort-by-Merge
Techniques 75
4.4 CatalanNumbers 77
4.5 Problems 82
5 FlowinNetworks 85
5.1 Introduction 85
5.2 TheAlgorithmofFordandFulkerson 87
5.3 TheDinitzAlgorithm 94
5.4 NetworkswithUpperandLowerBounds 102
5.5 Problems 109
5.6 NotesbyAndrewGoldberg 115
6 ApplicationsofNetworkFlowTechniques 117
6.1 Zero-OneNetworkFlow 117
6.2 VertexConnectivityofGraphs 121
6.3 ConnectivityofDigraphsandEdgeConnectivity 129
6.4 MaximumMatchinginBipartiteGraphs 135
6.5 TwoProblemsonPERTDigraphs 137
6.6 Problems 141
7 PlanarGraphs 146
7.1 BridgesandKuratowski’sTheorem 146
7.2 Equivalence 157
7.3 Euler’sTheorem 158
7.4 Duality 159
7.5 Problems 164
8 TestingGraphPlanarity 168
8.1 Introduction 168
8.2 ThePathAdditionAlgorithmofHopcroftandTarjan 169
8.3 Computinganst-Numbering 177
8.4 TheVertexAdditionAlgorithmofLempel,Even,and
Cederbaum 179
8.5 Problems 185
Index 187
Foreword
InAppreciationofShimonEven
Shimon was a great computer scientist who inspired generations of Israeli
stutents and young researchers, including many future leaders of theoretical
computerscience.
He was a master at creating combinatorial algorithms, constructions, and
proofs. He always sought the simplest and most lucid solutions. Because he
neverallowedhimselftouseaknowntheoremunlessheunderstooditsproof,his
discoverieswereoftenbasedonoriginalmethods.Hislectureswerelegendary
fortheirclarity.
Shimon was devoted to his family, generous to his colleagues, and freely
availabletothestudentsinhisclasses.
He expressedhisviewsforcefullyandwith completehonesty.He expected
honestyinreturn,andreservedhisdisapprovalforthosewhotriedtoobfuscate
ormislead.
Shimon hadan unendingsupplyof interesting anecdotes,and wouldlaugh
uproariouslyatgoodjokes,includinghisown.
Insum, hewas a greatandunforgettablemananda greatscientist, andhis
namehasapermanentplaceintheannalsoftheoreticalcomputerscience.
RichardM.Karp
Berkeley,April2011
vii