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1、CalculatingLinearTimeAlgorithmsforSolvingMaximumWeightsumProblemsIsaoSasanoZhenjiangHuMasatoTakeichiDepartmentofInformationEngineeringTheUniversityofTokyo(fsasano,hu,takeichig@ipl.t.u-tokyo.ac.jp)MizuhitoOgawaNTTCommunicationScienceLaboratories,NTT,Japan(mizuhito@theory.brl.ntt.c
2、o.jp)AbstractGroupOrganizingProblemThepresidentwantstoor-ganizeaprojectgroupinwhichtheexistingsupervisorInthispaper,weproposeanewmethodtoderivepracticalrelationcantakee ect;thatis,eachgroupmember(ex-lineartimealgorithmsformaximumweightsumproblems.Aceptthegroupleader)hashisorherdi
3、rectorindirectmaximumweightsumproblemisspeci edasfollows:givensupervisorinthegroup.arecursivedatax, ndanoptimalsubsetofelementsofxTheproblemistodesignalinearalgorithmtomakethewhichnotonlysatis escertainpropertypbutalsomaxi-memberlist.Again,thegoalshouldbetomaximizethemizesthesumo
4、ftheweightofelementsofthesubset.Thesumoftheconvivialityratingsofthemembers.keypointofourapproachistodescribethepropertypasafunctionalprogram.Thisenablesustouseprogramtrans-SupervisorChainingProblemThepresidentwantstoformationtechniques.Basedonthisapproach,wepresentawardachainofsu
5、pervisorswhosesumoftheconvivi-theoptimizationtheorem,withwhichweconstructasys-alityismaximum.tematicframeworktocalculateecientlineartimealgo-Theproblemistodesignalinearalgorithmtocomputerithmsformaximumweightsumproblemsonrecursivedatathesupervisorlist.structures.Wedemonstratee e
6、ctivenessofourapproachthroughseveralinterestingandnon-trivialexamples,whichwouldbediculttosolvebyknownapproaches.Theseproblems,thoughlookingabitdi erent,canbeformulatedinthefollowinguniformway:Givenatreetwithnodesbeingassociatedwithweights,Keywords:ProgrammingPearl,ProgramTransf
7、ormation,weareinterestedin ndingasetofnodesvs,whichsatis esCatamorphism,Mutumorphisms,LinearTimeGraphAlgo-acertainpropertyp(t;vs)andmaximizesthesumofnoderithm,Fusion,Tupling,OptimizationProblems,Dynamicweights,i.e.,Programming.spect=maximizeweightsum1Introduction[vsjvsnodest;p(t;
8、vs)]Considerthefollowingoptimizationprob
