機(jī)動(dòng)車安全技術(shù)檢驗(yàn)機(jī)構(gòu)檢驗(yàn)

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、靜夜夜四無(wú)無(wú)鄰，，荒居居舊業(yè)業(yè)貧。。。12月月-2212月月-22Wednesday,December28,202210、雨中黃葉葉樹(shù)，燈下下白頭人。。。21:19:3121:19:3121:1912/28/20229:19:31PM11、以我獨(dú)沈久久，愧君相見(jiàn)見(jiàn)頻。。12月-2221:19:3121:19Dec-2228-Dec-2212、故人人江海海別，，幾度度隔山山川。。。21:19:3121:19:3121:19Wednesday,December28,202213、乍乍見(jiàn)見(jiàn)翻翻疑疑夢(mèng)夢(mèng)，，相相悲悲各各問(wèn)問(wèn)年年。。。。12月月-2212月月-2221:19:3121:19:31December28,202214、他鄉(xiāng)生生白發(fā)，，舊國(guó)見(jiàn)見(jiàn)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、行動(dòng)出成成果，工作作出財(cái)富。。。2022/12/2821:19:3121:19:3128December202217、做做前前，，能能夠夠環(huán)環(huán)視視四四周周；；做做時(shí)時(shí)，，你你只只能能或或者者最最好好沿沿著著以以腳腳為為起起點(diǎn)點(diǎn)的的射射線線向向前前。。。。9:19:31下下午午9:19下下午午21:19:3112月月-229、沒(méi)有失敗，，只有暫時(shí)停停止成功！。。12月-2212月-22Wednesday,December28,202210、很多事情努努力了未必有有結(jié)果，但是是不努力卻什什么改變也沒(méi)沒(méi)有。。21:19:3121:19:3121:1912/28/20229:19:31PM11、成功功就是是日復(fù)復(fù)一日日那一一點(diǎn)點(diǎn)點(diǎn)小小小努力力的積積累。。。12月月-2221:19:3121:19Dec-2228-Dec-2212、世間成事事，不求其其絕對(duì)圓滿滿，留一份份不足，可可得無(wú)限完完美。。21:19:3121:19:3121:19Wednesday,December28,202213、不知香香積寺，，數(shù)里入入云峰。。。12月-2212月-2221:19:3121:19:31December28,202214、意志堅(jiān)強(qiáng)的的人能把世界界放在手中像像泥塊一樣任任意揉捏。28十二月月20229:19:31下午21:19:3112月-2215、楚塞三湘接接，荊門九派派通。。。十二月229:19下下午12月-2221:19December28,202216、少年十五二二十時(shí)，步行行奪得胡馬騎騎。。2022/12/2821:19:3121:19:3128December202217、空山山新雨雨后，，天氣氣晚來(lái)來(lái)秋。。。9:19:31下下午9:19下下午午21:19:3112月月-229、楊楊柳柳散散和和風(fēng)風(fēng)，，青青山山澹澹吾吾慮慮。。。。12月月-2212月月-22Wednesday,December28,202210、閱讀一一切好書(shū)書(shū)如同和和過(guò)去最最杰出的的人談話話。21:19:3121:19:3121:1912/28/20229:19:31PM11、越是沒(méi)有有本領(lǐng)的就就越加自命命不凡。12月-2221:19:3121:19Dec-2228-Dec-2212、越越是是無(wú)無(wú)能能的的人人，，越越喜喜歡歡挑挑剔剔別別人人的的錯(cuò)錯(cuò)兒兒。。21:19:3121:19:3121:19Wednesday,December28,