6 I \ No .co/-ptsreporteds . 440*1 & . . : 6 ' Layering . . - PowerPoint PPT Presentation

- , * - Dim Range Tree : Can we do better ? call this as Recap : .ge#TaYesi:socniogdiny-kTaFaesIr:uc9uerneFoartpPIsiPn Ran "kd rangetreewithf claim :A - Orthogonal range query - Query time : n pts has space Oln ) and : Oclogdn ) : - aligned answers ID range countlrept Countlreportpts in axis counting tins :m% 's :* :* . ⇒ me ? - Kristie : cnn.im . : combing search structures .jp ? iqetreej.IwM.kI Vnforlargen .pt ? o-efotrtede " " " t Report :O ! ktrn ) time → counts ! . . " ' → Range trees are i. ④ - . . more limited 6 I \ No .co/-ptsreporteds . 440*1 & . . : 6 ' Layering . . IQ " " * :* :g%Ywt . 'm : ¥ pEa Tommy ④ a ② ④ on 1 $ criteria : Quiz 24 Q . - medical data : Count subjects " . HI : awsagesani 3- Dim Range Tree : Canonical subsets Age range : ④ ' . . - Goal : Express . : wiosweightswni . codo8o8o%oboot_R Weight range answer as Q ! - law a data structure for disjoint union of subsets - Design . → Count :S : 'S " " each criterion individually - Method : Search for Qbs Rept Approach : - Layer these structures together - Balanced BST ( e.g Quite take maximal subtrees . AVL ,RD , to answer full query - Assume extended tree ←¥€¥€¥¥ "÷÷ " " " - Each node p stores , of no → multi-Layer Data structures entries 'm subtree :p . size , ° ,

- , I y - range x. range : Recursive helper , " " .is ? i::i&:k:iD-winoi:er:o:i.aniibeaoue ? .r..os...y :÷÷j ,op More details ÷÷ :/ : : D int range ID × ( Node p , a ID range tree T : Given initiate :i ¥ k9g :O - For each node p , define ④ Cases ÷tm Y ' :[ xo ,x , ] . ↳ Jlp ) interval cell C : sit .at/ptsotpssubtree2-DRange Searching is external p : : - ifp.pt .xEQ → 1 else → o a range tree forthwith lie in C " ' " Layer - - . . . : Costain ] - Root cell 's internal : range tree for y sina.ge ? Trees.'ImT..&F-Det:p.aux:AgypDjy pi - C 's Q ⇒ all of pi pts lie , let - For each node pelts - x tree - setofptsinps subtree within query Jlp ) - f.qreturnp.siz.pe tree for § € 1 1 ¥ If Analysis : int range ¥¥ ::x"i hesitantly . x( Node . II. tf IT p , doisipintm.ie ? ianone/ek:iYiIsP&Yr:En*p:i x nie - lawn :c " " :%imon :{ 91%1%75 : . ' disjoint ) return → return 0 ,p - else ( Qrc - Else partial overlap Dr Thm :GwenfDrangetreeT else ① return : ' ftp.xkirangeIDx/p.lett,Q,Exo,p.xD on pi children trangeldxlp.right.Q.lp.xsx.IT/tinieOClogn)......ftktorcport ) can answer range queries in → Recuse + trim the cell I . \ -

Answering Queries ? ,% ① Q - , " Higher Dimensions ? . .÷÷÷÷÷÷÷÷÷i÷÷ 2DRangeTree : - Construct ID range tree Given query range - Ind - dim space , we create d- layers on x words for all pts Q=[ Qw.x.Qhi.xIXLQio.y.Qhi.gl based - Each recuses - Run range IDX to find all - For each node p one dim lower : .÷÷÷÷÷÷÷÷÷÷:÷÷÷÷ i :* : - trees - range tree x-treetln.by :# ¥¥ i÷t÷ ¥ ÷÷÷÷i÷÷÷n x p.am , Analysis : The 3D xsearchtakes i. ⇒ sees :* :* :* :c :* DOVIDIO - login )=Odo5n ) : Ollogn ⇒ T otal - I :L :÷f÷t÷l÷ .li/.ani*s-ran*treeeisePiitceoit:n:ia::tisiP*to I '/ : ⑧ Em intrange2DCNodep.RectQ.Intvdslxo.x.NL Analysis Qhiix Qioix :& : ¥ ÷÷e .in . - faith ] " init y - cell ← Invoked Oclogn ) ( return rangel.dz/p.aux,Q,Cyo,yD ) [ ' yo ,y , ) - - Qw , times - once - layer finds lelseifCQ.is disjoint of Pwafffeaeximal : The x Intuition return 0 - range subtrees else llpartialx - overlap p contained in x return range2Dlp.lett.Q.cxo.p.is ) Ihfifnke ! % ¥ 9fo ? + each aux tree filters based t rangc2D( p . right ,Q,[ pix , X , ] ) on y each ancestor of . g subtree Max - .