机动车安全技术检验机构检验

Chapter4Partition(1)ShiftingDing-ZhuDuDiskCoveringGivenasetofnpointsintheEuclideanplane,findtheminimumnumberofunitdiskstocoverthengivenpoints.(x,x)PartitionP(x)aConstructMinimumUnitDiskCoverinEachCell1/√2Eachsquarewithedgelength1/√2canbecoveredbyaunitdisk.Hence,eachcellcanbecoveredByatmostdisks.

Supposeacellcontainsnipoints.Thenthereareni(ni-1)possiblepositionsforeachdisk.MinimumcovercanbecomputedIntimeniO(a)2SolutionS(x)associatedwithP(x)Foreachcell,constructminimumcover.S(x)istheunionofthoseminimumcovers.Supposenpointsaredistributedintokcellscontainingn1,…,nkpoints,respectively.ThencomputingS(x)takestimen1+n2+···+nk

<nO(a)O(a)O(a)O(a)2222ApproximationAlgorithmForx=0,-2,…,-(a-2),computeS(x).ChooseminimumonefromS(0),S(-2),…,S(-a+2).AnalysisConsideraminimumcover.Modifyittosatisfytherestriction,i.e.,aunionofdiskcoverseachforacell.Todosuchamodification,weneedtoaddsomedisksandestimatehowmanyaddeddisks.AddedDisksCounttwiceCountfourtimes22ShiftingEstimate#ofaddeddisksShiftingEstimate#ofaddeddisksVerticalstripsEachdiskappearsonce.Estimate#ofaddeddisksHorizontalstripsEachdiskappearsonce.Estimate#ofaddeddisks#ofaddeddisksforP(0)+#ofaddeddisksforP(-2)+·····+#ofaddeddisksforP(-a+2)<3optwhereoptis#ofdiskinaminimumcover.Thereisaxsuchthat#ofaddeddisksforP(x)<(6/a)opt.PerformanceRatioP.R.<1+6/a<1+εwhenwechoosea=6⌠⌠1/ε.Runningtimeisn.O(1/ε)2Unitdiskgraph<1DominatingsetinunitdiskgraphGivenaunitdiskgraph,findadominatingsetwiththeminimumcardinality.TheoremThisproblemhasPTAS.ConnectedDominatingSetinUnitDiskGraphGivenaunitdiskgraphG,findaminimumconnecteddominatingsetinG.TheoremThereisaPTASforconnecteddominatingsetinunitdiskgraph.Boundaryareacentralareahh+1Whyoverlapping?cdsforGcdsforeachconnectedcomponent11.Ineachcell,constructMCDSforeachconnectedcomponentintheinnerarea.ConstructPTAS2.Connectthoseminimumconnecteddominatingsetswithapartof8-approximationlyinginboundaryarea.ForeachpartitionP(a,a),constructC(a)asfollows:ChoosesmallestC(a)fora=0,h+1,2(h+1),…….Existenceof8-approximationThereexists(1+ε)-approximationforminimumdominatingsetinunitdiskgraph.2.Wecanreduceoneconnectedcomponentwithtwonodes.Therefore,thereexists3(1+ε)-approximationformcds.8-approximationAmaximalindependentsethassizeatmost4mcds+1.2.Thereexistsamaximalindependentset,connectingitintocdsneedatmost4mcdsnodes.MCDS(Time)Inasquareofedgelength,anynodecandominateeverybodeinthesquare.Therefore,minimumdominatingsethassizeatmost.aMCDS(Time)2.ThetotalsizeofMCDSsforconnectedcomponentsinaninnersquareareaisatmost.aMCDS(Size)ModifyamcdsforGintoMCDSsineachcell.mcds(G):mcdsforGmcdscell(inner):MCDSinacellforconnectedcomponentsininnerareaConnect&ChargechargeMultipleChargechargeHowmanypossiblechargesforeachnode?Howmanycomponentscaneachnodebeadjacentto?1.Howmanyindependentpointscanbepackedbyadiskwithradius1?1>15!Eachnodecanbechargedatmost10times!!!Shifting3a/(2(h+1))=integerTime=nO(a)2h=2WeightedDominatingSetGivenaunitdiskgraphwithvertexweight,findadominatingsetwithminimumtotalweight.Canthepartitiontechniquebeusedfortheweighteddominatingsetproblem?DominatingSetinIntersectionDiskGraphAnintersectiondiskgraphisgivenbyasetofpoints(vertices)intheEuclideanplane,eachassociatedwithadiskandanedgeexistsbetweentwopointsifftwodisksassociatedwiththemintersects.Canthepartitiontechniquebeusedfordominatingsetinintersectiondiskgraph?Thanks,End9、静夜夜四无无邻，，荒居居旧业业贫。。。12月月-2212月月-22Wednesday,December28,202210、雨中黄叶叶树，灯下下白头人。。。21:19:3121:19:3121:1912/28/20229:19:31PM11、以我独沈久久，愧君相见见频。。12月-2221:19:3121:19Dec-2228-Dec-2212、故人人江海海别，，几度度隔山山川。。。21:19:3121:19:3121:19Wednesday,December28,202213、乍乍见见翻翻疑疑梦梦，，相相悲悲各各问问年年。。。。12月月-2212月月-2221:19:3121:19:31December28,202214、他乡生生白发，，旧国见见青山。。。28十十二月20229:19:31下午午21:19:3112月-2215、比不了得就就不比，得不不到的就不要要。。。十二月229:19下下午12月-2221:19December28,202216、行动出成成果，工作作出财富。。。2022/12/2821:19:3121:19:3128December202217、做做前前，，能能够够环环视视四四周周；；做做时时，，你你只只能能或或者者最最好好沿沿着着以以脚脚为为起起点点的的射射线线向向前前。。。。9:19:31下下午午9:19下下午午21:19:3112月月-229、没有失败，，只有暂时停停止成功！。。12月-2212月-22Wednesday,December28,202210、很多事情努努力了未必有有结果，但是是不努力却什什么改变也没没有。。21:19:3121:19:3121:1912/28/20229:19:31PM11、成功功就是是日复复一日日那一一点点点小小小努力力的积积累。。。12月月-2221:19:3121:19Dec-2228-Dec-2212、世间成事事，不求其其绝对圆满满，留一份份不足，可可得无限完完美。。21:19:3121:19:3121:19Wednesday,December28,202213、不知香香积寺，，数里入入云峰。。。12月-2212月-2221:19:3121:19:31December28,202214、意志坚强的的人能把世界界放在手中像像泥块一样任任意揉捏。28十二月月20229:19:31下午21:19:3112月-2215、楚塞三湘接接，荆门九派派通。。。十二月229:19下下午12月-2221:19December28,202216、少年十五二二十时，步行行夺得胡马骑骑。。2022/12/2821:19:3121:19:3128December202217、空山山新雨雨后，，天气气晚来来秋。。。9:19:31下下午9:19下下午午21:19:3112月月-229、杨杨柳柳散散和和风风，，青青山山澹澹吾吾虑虑。。。。12月月-2212月月-22Wednesday,December28,202210、阅读一一切好书书如同和和过去最最杰出的的人谈话话。21:19:3121:19:3121:1912/28/20229:19:31PM11、越是没有有本领的就就越加自命命不凡。12月-2221:19:3121:19Dec-2228-Dec-2212、越越是是无无能能的的人人，，越越喜喜欢欢挑挑剔剔别别人人的的错错儿儿。。21:19:3121:19:3121:19Wednesday,December28,