
soonn sidhaantham

jyamithiyil, oru variyude mekhalayude sankeernnatha rekhakalude krameekaranatthil sthaapikkunna falamaanu soonn sidhaantham.
nirvachanam.
formula _ 1 ennu soochippikkunna oru "line krameekaranam", oru koottam lainukalude formula _ 2, cellukal (formula _ trimana mukhangal), arikukal (formula _ 4-dimensional mukhangal), konukal (formula _ 5-dimensional mukhangal) ennivayilekku prerippikkunna thalatthinte oru upavibhagamaanu. formula _ 6 lines formula _ 2, line krameekarana formula _ 1, oru line formula _ 9 (formula _ 2-ll ulppedaatha) enniva nalkiyaal, formula _ 9-nte "soonn" formula _ 9-ll murichukadakkunna mukhangalude koottamaanu. oru soninte "sankeernnatha" ennathu athinte athirthiyile attangalude aake ennamaanu, ithu formula _ 6-nte pravartthanamaayi prakadippikkunnu.
sankeernnatha soothravaakyam _ 14 aanennu soonn sidhaantham prasthaavikkunnu.
charithram.
eee phalam aadyamaayi prasidheekarichathu 1985-laanu; chassellum mattullavarum. oru krameekaranatthile oru variyude mekhalayude sankeernathaykku formula _ 15-nte mukalile paridhi nalki. 1991-ll, eee boundu formula _ 16 aayi mechappeduthi, koodaathe ithu oru cheria additteev factor vare saadhyamaaya ettavum mikacha upper boundu aanennum kaanichu. thudarnnu, 2011-ll, oru krameekaranatthile oru variyude mekhalayude sankeernnatha paramavadhi soothravaakyam _ 17 aanennum ithu oru irukiya bandhamanennum roome pinchasi theliyichu.
sidhaanthathinte vyathyastha thelivukalil upayogikkunna chila maathrkakal induction, sweep technic, trea kanstrakshan, davenport-shinzell sequenceukal ennivayaanu.
saamaanyavalkkaranangal.
ettavum janapriyamaaya pathipp thalatthile varikalude krameekaranamaanengilum, soonn sidhaanthathinte chila saamaanyavalkkaranangal nilavilundu. udaaharanathinu, hyperplayinukalude krameekaranangal pariganichu, hyperplane formula 19-nte soninte sankeernnatha, formula 19 kondu murichukadakkunna koshangalude koottatthe (formula 18-dimensional faceukal) bandhippikkunna vashangalude ennamaanu (formula 20-dimensional faceukal). samaanamaayi, formula 18-dimensional soonn sidhaantham oru hyperplaininte soninte sankeernnatha formula 24 aanennu prasthaavikkunnu. dimension formula 25-nulla sidhaanthathinu ganyamaaya thelivukal kuravaanu. formula 26-dimensional kesil, sweep teknikkukale adisthaanamaakkiyulla thelivukalundu, uyarnna alavukalkku yoolarinte bandham upayogikkunnu
soothravaakyam _ 27
mattoru saamaanyavalkkaranam varikalkkum (hyperplayinukalkkum) pakaram syoodolinukalude (alavukal formula _ 18-ll seudohyperplayinukal) krameekaranangal pariganikkuka ennathaanu. sidhaanthathinte chila thelivukal eee saahacharyathil nannayi pravartthikkunnu, kaaranam avaa avarude vaadangaliloode varikalude nerthathvam ganyamaayi upayogikkunnilla.
prachodanam.
krameekaranangalile soonn sankeernnatha padikkunnathinulla praadhamika prachodanam krameekaranangal nirmmikkunnathin kaaryakshamamaya algorithangal thedunnathil ninnaan undaakunnath. classical algoritam ennathu incremental nirmmaanamaan, ithu onninupurake onnaayi varikal cherkkunnathum oronnum srishtikkunna ellah mukhangalum uchithamaaya dattaa ghadanayil sambharikkunnathum aayi vivarikkaam (krameekaranangalude saadhaarana ghadana eratti connectucheytha edju listt (dii. ezz. ell) aanu). ivide, soonn sidhaanthathinte anantharafalam, formula _ 6 varikalude eathu krameekaranatthinteyum muzhuvan nirmmanavum time formula _ 30 ll cheyyaan kazhiyum ennathaanu, kaaranam oro variyum ulppeduthunnathinu time formula _ 14 edukkum.