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1、EuclideanShortestPathsÒBeautyonthePathÓ,adigitalpaintingbyStephenLi(Auckland,NewZealand),September2011,providedasagiftforthisbook.FajieLiReinhardKletteEuclideanShortestPathsExactorApproximateAlgorithmsFajieLiReinhardKletteSchoolofInformationScienceDept.ComputerScienceandTechnologyUniversityofAuc
2、klandHuaqiaoUniversityP.O.Box92019P.O.Box800Auckland1142XiamenFujianNewZealandPeopleÕsRepublicofChinar.klette@auckland.ac.nzli.fajie@yahoo.comISBN978-1-4471-2255-5e-ISBN978-1-4471-2256-2DOI10.1007/978-1-4471-2256-2SpringerLondonDordrechtHeidelbergNewYorkBritishLibraryCataloguinginPublicationDataA
3、cataloguerecordforthisbookisavailablefromtheBritishLibraryLibraryofCongressControlNumber:2011941219©Springer-VerlagLondonLimited2011Apartfromanyfairdealingforthepurposesofresearchorprivatestudy,orcriticismorreview,asper-mittedundertheCopyright,DesignsandPatentsAct1988,thispublicationmayonlyberepr
4、oduced,storedortransmitted,inanyformorbyanymeans,withthepriorpermissioninwritingofthepublish-ers,orinthecaseofreprographicreproductioninaccordancewiththetermsoflicensesissuedbytheCopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethosetermsshouldbesenttothepublishers.Theuseofregistere
5、dnames,trademarks,etc.,inthispublicationdoesnotimply,evenintheabsenceofaspeciÞcstatement,thatsuchnamesareexemptfromtherelevantlawsandregulationsandthereforefreeforgeneraluse.Thepublishermakesnorepresentation,expressorimplied,withregardtotheaccuracyoftheinformationcontainedinthisbookandcannotaccep
6、tanylegalresponsibilityorliabilityforanyerrorsoromissionsthatmaybemade.Coverdesign:VTeXUAB,LithuaniaPrintedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)ToZhixingLi,andtothetwoyoungestintheKlettefamilyinNewZealandForewordTheworldiscontinuousthemindisdiscrete.David
7、Mumford(born1937)Recently,IwasconfrontedwiththeproblemofplanningmytravelfromIsraeltoNewZealand,homeofthetwoauthorsofthisbook.Whentakingtwoantipodalpointsontheglobe,likeHaifaandQueenstown,thereisaninÞnitenumberofshort-e