keey-sanch (bhoomiti)

swatantra bhoomitimadhye, euclidean pratalatil maryadit bindu sanch sootra _ 2 chaa sootra _ 1-sanch haah sootra _ 2 chya sootra _ 1 ghatakancha upasanch aahe joou urvarit bindunpasoon reshedvare katekorpane vegala keela jaau shakato. adhik samanyatah, uchch parimananchya euclidean jaaget, maryadit bindu sanchatil sootra _ 1-sanch haah sootra _ 1 ghatakancha upasanch asato joou hyperplanedware urvarit bindunpasoon vegala keela jaau shakato. visheshtah, jevha sootra 7 (jethe sootra 8 heey sootra 2 chaa aakar aahe), tevha sootra 1-sanchala urvarit sootra 2 pasoon vegale karnari resha kinwa hyperplane hii ardharesha kinwa ardh samtal asate.
samatalatil bindunchya sanchache sootra _ 1-sanch reshanchya vyavasthetil sootra _ 1-staranshi prakshepak dwaitatedware sambandhit asatat. samatalatil sootra 8 reshanchya rachneteel sootra 1-patali hii vakr aahe jyat eka reshevar asalelya binduncha samavesh asato aanee tyanchya khalee nemke sootra 1 resha asatat. swatantra aanee sanganakeey bhoomitine adhik samanya prakarchya vakr aanee prushthbhaganchya vyavasthetil patalicha dekhil abhyas keela aahe.
sanyukt seema.
bhoomitiy algoridamchya vishleshanamadhye samtol bindu sanchatil sootra _ 1-sanchanchi sankhya kinwa samtol reshechya vyavasthechya sootra _ 1-staranchi sankhya, hii samasya pratham lovas aanee erdos aanee itaranni abhyasali, tee bandhane mahattvache aahe. yaa samasyesathi sarvat prasiddha varchi seema sootra 19 aahe, jee tamal deyne ajtai, chwatal, navjat aanee szemereddy yanchya crassing nambarchya asamanatecha vapar karoon darshavili aahe. tathapi, sarvat prasiddha khalchi seema hii dii. eae. chya varchya maryadepasoon khoop door aaheh tothdware darshavilyapramane, kahee sthir sutrasathi heey sootra _ 20 aahe.
teen parimananmadhye, sarvat changli varchi seema sootra _ 22 aahe aanee sarvat changli khalchi seema sootra _ 23 aahe.
uttal sthiteet asalelya teen parimananmadhil bindunsathi, mhanje, kahee uttal bahupadiche shirobindu aahet, sootra _ 1-sanchanchi sankhya aahe 
sootra _ 25, jeey sootra _ _ kramachya voronoi aakrutinchya guntaguntila bandhanyasathi vaparlya jaanarya yuktivadanche anusaran karate.
jevha sootra _ 7 (ardhya resha) asate, tevha sootra _ 2 chya done bindundware sanyuktapane bhinn reshanchi kamal sankhya jee sootra _ 29 asatana urvarit bindunna dwibhajit karate
sootra _ 30-sanchanchya sankhyevarhi seema siddha jhalya aahet, jethe sootra _ 30-sanch heey kahee sootra _ 33 sathee sootra _ 32-sanch aahe. done parimananmadhye, sootra _ 30-sanchanchi kamal sankhya tantotant sootra _ 35 aahe, tarr sootra _ 36 parimananmadhye seema sootra _ 37 aahe.
bandhkam algoridam.
edelsbrunner aanee welzel yanni pratham input point sanchatil serve sootra _ 1 sanch tayar karnyachya samasyecha abhyas keela, kinwa vyavastheche sootra _ 1 star tayar karnyachya samasyecha abhyas keela. tyanchya algoridamchi formula _ 1-stariy aavrutti plain sweep algoridam mhanoon pahili jaau shakate jee davikadoon ujavikade kramvarit patali tayar karate. bindu sanchanchya sootra _ 1-sanchanchya drushtine pahile tarr, tyanche algoridam vegalya reshechya pratyek bajuchya bindunsathi eka gatishil bahirmukh patangachi dekhbhal karate, varanvar yaa done patangacha eka betangent shodhate aanee sparshikechya done bindunpaiki pratyekala viruddha patangachya dishene halavate. chaan yaa samasyechya tyanantarchya parinamanche sarvekshan karato aanee darshavito qee heey sootra _ 1-patalichya guntaguntivar bandhalelya dii. eae. chya sootra _ 19 chya pramanat velevar sodavale jaau shakate.
aagarwal aanee matausek yanni andaje patali karyakshamatene tayar karnyasathi algoridamche varnan kele aahe; mhanje, kahee lahan andaje mapdand sutrasathi sootra 44-patali aanee sootra 45-patali darmyan jaanara eka vakr. teey darshavtat qee assa andaj aadhalu shakato, jyamadhye anek resha vibhag asatat jeey fakt sootra 47 varr avalambun asatat aanee sootra 8 kinwa sootra 1 varr avalambun nasatat.
matroid samanyikaran.
samtol sootra _ 1-stariy samasyeche matroidmadhil parametric optimizationmadhe samanyikaran kele jaau shakateh ekhadyala eka matroid dile jaate jyamadhye pratyek ghatak parameter sootra _ 51 chya resheey karyadvare bharit keela jaato aanee sootra _ 51 chya pratyek sambhavya mulyasathi matroidcha kiman vajan aadhar shodhane aavashyak aahe. jarr ekhadyane vajan karyanna pratalatil resha mhanoon aalekh kele tarr yaa reshanchya rachanecha formula _ 1 star sootra _ 51 chey karya mhanoon aalekh karato, eksaman matroidmadhye ishtatam aadharavaril sarvat mothya ghatakache vajan, aanee dii. eae. neey darshavile qee sootra _ 1-patalichya jatilatevar bandhalele tyache sootra _ 19 heey sootra _ 8 ghatak aanee shreni sootra _ 1 saha konatyahi matroidchya vishisht ishtatam aadharanchi sankhya mojanyasathi samanyikaran kele jaau shakate.
udaharanarth, tech sootra _ 19 varchya simareshevar, sootra _ 8 kadaa aanee sootra _ 1 shirobindu asalelya aalekhamadhye tayar jhalelya vegvegalya kiman pasarlelya zadanchi sankhya mojanyasathi lagoo hote, jevha kathanvar vajan asate jeey parameter sootra _ 51 saha reshiyaritya badalate. yaa parametric kiman pasarlelya vruksh samasyecha abhyas vividh lekhakanni keela aahe aanee tyacha vapar vruksh optimization itar dvi-criterian pasarlelya samasyanche nirakaran karnyasathi keela jaau shakato.
tathapi, parametric kiman vistar vruksh samasyesathi sarvat prasiddha loar bound mhanje formula _ 63, formula _ 1-seet samasyepeksha kamkuvat bound. adhik samanya matroidsathi, dii. eae. chya _ 19 yaa varchya bandhanat julanari khalchi bandhane asatat.

