Combinatorial Optimization: Theory and Algorithms

679 Pages·2012·4.66 MB·English

by  Bernhard Korte

Algorithms and Combinatorics
Volume 21
EditorialBoard
RonaldGraham
BernhardKorte
LászlóLovász
AviWigderson
WilliamJ.Cook
GünterM.Ziegler

Forfurthervolumes:
http://www.springer.com/series/13
•
Bernhard Korte Jens Vygen
(cid:2)
Combinatorial Optimization
Theory and Algorithms
Fifth Edition

123
BernhardKorte
JensVygen
UniversityofBonn
ResearchInstitutefor
DiscreteMathematics
Lennéstr.2
53113Bonn
Germany
[e-mail]
[e-mail]

AlgorithmsandCombinatoricsISSN0937-5511
ISBN978-3-642-24487-2 e-ISBN978-3-642-24488-9
DOI10.1007/978-3-642-24488-9
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2011945680
MathematicsSubjectClassification(2010):90C27,68R10,05C85,68Q25
(cid:2)c Springer-VerlagBerlinHeidelberg2000,2002,2006,2008,2012
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Preface to the Fifth Edition
Whenpreparingthefirsteditionofthisbook,morethantenyearsago,wetriedto
accomplishtwoobjectives:itshouldbeusefulasanadvancedgraduatetextbook,but
alsoasareferenceworkforresearch.Witheachneweditionwehavetodecidehow
thebookcanbeimprovedfurther.Ofcourse,itislessandlesspossibletodescribe
thegrowingareacomprehensively.

If we included everything that we like, the book would grow beyond a single
volume. Since the book is used for many courses, now even sometimes at under-
graduatelevel,wethoughtthataddingsomeclassicalmaterialmightbemoreuseful
thanincludingaselectionofthelatestresults.
Inthisedition,weaddedaproofofCayley’sformula,moredetailsonblocking
flows,thenewfasterb-matchingseparationalgorithm,anapproximationschemefor
multidimensionalknapsack,andresultsconcerningthe multicommoditymax-flow
min-cutratioandthesparsestcutproblem.Therearefurthersmallimprovementsin
numerousplacesand morethan 60new exercises.Of course,we also updatedthe
referencesto pointtothemostrecentresultsandcorrectedsomeminorerrorsthat
werediscovered.
We would like to thank Takao Asano, Maxim Babenko, Ulrich Brenner,
Benjamin Bolten, Christoph Buchheim, Jean Fonlupt, András Frank, Michael
Gester, Stephan Held, Stefan Hougardy, Hiroshi Iida, Klaus Jansen, Alexander
Karzanov,LevinKeller,AlexanderKleff,NikoKlewinghaus,StefanKnauf,Barbara
Langfeld, Jens Maßberg, Marc Pfetsch, Klaus Radke, Rabe von Randow, Tomás
Salles, Jan Schneider, Christian Schulte, András Sebo˝, Martin Skutella, Jácint
Szabó,andSimonWedekingforvaluablefeedbackonthepreviousedition.
Wearepleasedthatthisbookhasbeenreceivedsowell,andfurthertranslations
areontheirway.EditionsinJapanese,French,Italian,German,Russian, andChi-
nese haveappearedsince 2009or arescheduledto appearsoon.We hopethatour
book will continue to serve its purpose in teaching and research in combinatorial
optimization.
Bonn,September2011 BernhardKorteandJensVygen
V
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Preface to the Fourth Edition
With four English editions, and translations into four other languages forthcom-
ing,weareveryhappywiththedevelopmentofourbook.Again,wehaverevised,
updated,andsignificantlyextendeditforthisfourthedition.We haveaddedsome
classicalmaterialthatmayhavebeenmissedsofar,inparticularonlinearprogram-
ming,thenetworksimplexalgorithm,andthemax-cutproblem.Wehavealsoadded

a numberof new exercisesand up-to-datereferences.We hopethat these changes
servetomakeourbookanevenbetterbasisforteachingandresearch.
We gratefully acknowledge the continuous support of the Union of the Ger-
man Academies of Sciences and Humanities and the NRW Academy of Sciences
via the long-term research project “Discrete Mathematics and Its Applications”.
We also thank those who gave us feedback on the third edition, in particular
Takao Asano, Christoph Bartoschek, Bert Besser, Ulrich Brenner, Jean Fonlupt,
SatoruFujishige,MarekKarpinski,JensMaßberg,DenisNaddef,SvenPeyer,Klaus
Radke, Rabe von Randow, Dieter Rautenbach,Martin Skutella, Markus Struzyna,
Jürgen Werber, Minyi Yue, and Guochuan Zhang, for their valuable comments.
At http://www.or.uni-bonn.de/(cid:3)vygen/co.html we will continue
tomaintainupdatedinformationaboutthisbook.
Bonn,August2007 BernhardKorteandJensVygen
VII
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Preface to the Third Edition
After five years it was time for a thoroughly revised and substantially extended
edition.Themostsignificantfeatureisacompletelynewchapteronfacilitylocation.
Noconstant-factorapproximationalgorithmswereknownforthisimportantclassof
NP-hardproblemsuntileightyearsago.Todaythereareseveralinterestingandvery
differenttechniquesthatleadtogoodapproximationguarantees,whichmakesthis

areaparticularlyappealing,alsoforteaching.Infact,thechapterhasarisenfroma
specialcourseonfacilitylocation.
Manyoftheotherchaptershavealsobeenextendedsignificantly.Thenewmate-
rialincludesFibonacciheaps,Fujishige’snewmaximumflowalgorithm,flowsover
time,Schrijver’salgorithmforsubmodularfunctionminimization,andtheRobins-
ZelikovskySteinertreeapproximationalgorithm.Severalproofshavebeenstream-
lined,andmanynewexercisesandreferenceshavebeenadded.
Wethankthosewhogaveusfeedbackonthesecondedition,inparticularTakao
Asano,YasuhitoAsano,UlrichBrenner,StephanHeld,TomioHirata,DirkMüller,
Kazuo Murota, Dieter Rautenbach, Martin Skutella, Markus Struzyna and Jürgen
Werber, for their valuable comments. Eminently, Takao Asano’s notes and Jürgen
Werber’sproofreadingofChapter22helpedtoimprovethepresentationatvarious
places.
Again we would like to mention the Union of the German Academies of Sci-
encesandHumanitiesandtheNorthrhine-WestphalianAcademyofSciences.Their
continuoussupportviathelong-termproject“DiscreteMathematicsandItsAppli-
cations”fundedby the GermanMinistryof EducationandResearch and the State
ofNorthrhine-Westphaliaisgratefullyacknowledged.
Bonn,May2005 BernhardKorteandJensVygen
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