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.[1]{Æv=Frs|wm8-/0[J].ntxoy0,2008,34(4):31–[J].SouthChinaJournalofPreventiveMedicine,2008,34(4):31–32.[2]z}p, !8-/05vt=Æv8-/0[J].rsvtuV,2007,9:20–,-rials[J].MacroeconomicManagement,2007,9:20–22.[3]wxy,q( wm8-/05(xyuz[J].8z$w,2009(2):39–,[J].LogisticsSci-Tech,2009(2):39–41.[4]vx{,yzw,,.o{8-||/0,<3'[J].[KNTVW=LO,2007,27(4):91–,XieJC,[J].SystemsEngineering—Theory&Practice,2007,27(4):91–98.[5]{G$,q|.}x}+s| /0yz(1.{~=LÆ[J].|,}NT,2003,29(5):166–,[J].ComputerEngineering,2003,29(5):166–167.[6] !")P8;P~{(~|)J~*}rP[J]. L;}~y*~ ,2007,14(12):48–(12),Medicineofparasiticdiseases[J].ChinesePracticalJournalofRuralDoctor,2007,14(12):48–51.[7][J].OperationsReserchLetters,1991(10):417–419.[8]-assignmentproblems[J].JournalofSystemsScienceandSystemsEngineering,1997,6(1):1–4.[9]GareyMR,:AGuidetotheTheoryofNP-Completeness[M].SanFrancisco:,1979.[10]KorteB,—TheoryandAlgorithms[M].BerlinHeidelbergNewYork:Springer-Verlag,2002:361.