Combinatorial Optimization: Theory and Algorithms PDF
Preview Combinatorial Optimization: Theory and Algorithms
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 [email protected] [email protected] 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 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneral descriptive names,registered names, trademarks, etc. inthis publication does not imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotective lawsandregulationsandthereforefreeforgeneraluse. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) 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 • 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 • 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 IX
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