nikatatam padosi khoj

nikatata khoj key roop mein nikatatam padosi khoj (aine. aine. aiss.), diye gaye sett mein bindu khojane kii anukoolan samasya haye joe kissy diye gaye bindu key nikatatam (yaa sabse samaan) haye. nikatata koo aam taur parr ack bhinnata falan key sandarbh mein vyakt kiya jaataa haih vastuon key samaan cumm, falan moolyon mein badaa. 
aupchaarik roop seey, nikatatam-padosi (nn) khoj samasya koo nimnanusar paribhaashit kiya gayaa haih ack sthaan "aim" mein binduon kaa ack sett aur ack prashn bindu "kyu" ω "aim" diye jaane parr, "aiss" seey "kyu" mein nikatatam bindu khojen. wall mein donald naath. computer prograaming kii kalaa" (1973) key 3 ney ise dakghar kii samasya kahaa, joe nikatatam dakghar koo ack nivaas koo nirdisht karane key aavedan kaa ullekh kartaa haye. iss samasya kaa ack pratyaksh saamaanyikaran ack "key"-nn khoj haye, jahan hamein "key" nikatatam binduon koo khojane kii aavashyakta haye.
sabse aam taur parr "m" ack metrick sthaan haye aur visangati koo ack doori metrick key roop mein vyakt kiya jaataa haye, joe samamit haye aur tribhuj asamaanta koo santusht kartaa haye. isase bhee adhik samanya, "m" koo "d"-ayami sadish sthaan maanaa jaataa haye jahan euclidean doori, mainhattan doori yaa anya doori metrick kaa upayog karke bhinnata koo maapa jaataa haye. haalaanki, visangati kaary manmana hoe sakata haye. ack udaaharan asmamit bregman vichalan haye, jisake liye tribhuj asamaanta naheen haye.
anuprayog.
nikatatam padosi khoj samasya anuprayog key kaee kshetron mein utpann hoti haye, jinamen shamil hainh
vidhiyaan.
aine. aine. aiss. samasya key vibhinn samadhan prastaavit kiye gaye hain. algorithm kii gunavatta aur upayogita prashnon kii samay jatilata key saath-saath kissy bhee khoj detta sanrachana kii sthaan jatilata seey nirdhaarit hoti haye jise banaae rakhaa jaanaa chaahiye. anaupchaarik avalokan jise aamtaur parr ayamita key abhishaap key roop mein sandarbhit kiya jaataa haye, bataata haye kii bahupad poorv-prasanskaran aur bahupad khoj samay kaa upayog karke uchch-ayami euclidean sthaan mein aine. aine. aiss. key liye koee samanya-uddeshya sateek samadhan naheen haye.
sateek tareeke.
raikhik khoj.
aine. aine. aiss. samasya kaa sabse saral samadhan databases mein querry bindu seey harr dusare bindu taka kii doori kii ganana karna haye, "abb taka key sarvshreshth" kaa dhyaan rakhna haye. iss algorithm, jise kabhi-kabhi saral drishtikon key roop mein sandarbhit kiya jaataa haye, mein "oh" ("dn") kaa ack chalane kaa samay hotaa haye, jahaan "aine" "aiss" kii mukhyata haye aur "dee" "aiss" kii ayamita haye. banaae rakhane key liye koee khoj detta sanrachana naheen haye, isaliye raikhik khoj mein databases key bhandaran seey parey koee sthaan jatilata naheen haye. saral khoj, ausatan, uchch ayami sthaanon parr sthaan vibhajan drishtikon koo behtar banaa sakati haye.
doori kii tulanaa key liye nirpeksh doori kii aavashyakta naheen haye, kewal saapeksh doori. jyaamitiya nirdeshank pranaliyon mein dou nirdeshankon key beach kii doori kii ganana seey vargamool kii ganana koo chhodkar doori kii ganana koo kaafee badhaaya jaa sakata haye. doori kii tulanaa seey abhee bhee samaan parinam milenge.
space vibhajan.
1970 key dashak seey, shakha aur baadhya paddhati koo samasya parr lagu kiya gayaa haye. euclidean sthaan key mamle mein, iss drishtikon mein sthaanik soochkaank yaa sthaanik pahunch vidhiyaan shamil hain. aine. aine. aiss. samasya koo hull karane key liye kaee antariksh-vibhajan vidhiyaan vikasit kii gaee hain. shayed sabse saral key-dee vriksh haye, joe khoj sthaan koo mool kshetra key aadhe binduon vaale dou kshetron mein vibhajit kartaa haye. pratyek vibhajan parr prashn bindu kaa mulyankan karke pedh key jarh seey ack patte taka key pargaman key madhyam seey prashn kiye jaate hain. prashn mein nirdisht doori key aadhar parr, padosi shaakhaon mein hitt bhee hoe sakate hain jinka mulyankan karane kii aavashyakta hoe sakati haye. nirantar ayam prashn samay key liye, yaadrichhik roop seey vitarit binduon key mamle mein ausat jatilata "oh" (logg "aine") haye, sabse kharaab sthiti jatilata "oh" ("kn" ^ (1-1/"key")) haye.
vaikalpik roop seey aar-tree detta sanrachana koo gatishil sandarbh mein nikatatam padosi khoj kaa samarthan karane key liye design kiya gayaa thaa, kyonki isamen aar * tree jaise sammilan aur vilopan key liye kushal algorithm hain. aar-pedh naa kewal euclidean doori key liye nikatatam padosiyon koo utpann curr sakate hain, balki anya doori key saath bhee upayog kiya jaa sakata haye.
samanya metrick sthaan key mamle mein, shakha-aur-baadhya drishtikon koo metrick tree drishtikon key roop mein jaanaa jaataa haye. vishesh udaharanon mein vee. pee.-tree aur bee. key.-tree vidhiyaan shamil hain.
ack tri-ayami sthaan seey liye gaye binduon key ack samooh kaa upayog karke aur ack bee. aiss. pee. tree mein daal diyaa jaataa haye, aur usee sthaan seey liye gaye ack prashn bindu koo dekhate hue, prashn bindu key nikatatam bindu-baadal bindu koo khojane kii samasya kaa ack sambhaavit samadhan ack algorithm key nimnalikhit vivaran mein diyaa jaataa haye. 
(sakhti seey kahein tou aisaa koee bindu maujood naheen hoe sakata haye, kyonki yeh advitiya naheen hoe sakata haye. lekin vyavhaar mein, aamtaur parr humm kewal sabhi bindu-baadal binduon key kissy bhee upasamuchchay koo khojane kii parwah karate hain joe kissy diye gaye prashn bindu seey sabse cumm doori parr maujood hain.) vichaar yeh haye kii pedh kii pratyek shakha key liye, anuman lagaaen kii baadal mein nikatatam bindu prashn bindu vaale aadhe sthaan mein rahata haye. yeh mamla naheen hoe sakata haye, lekin yeh ack achchha shodh haye. anuman lagaae gaye aadhe sthaan key liye samasya koo hull karane kii sabhi samasyaon koo punaraavarti roop seey paar karane key baad, abb iss parinam dwara lauti gaee doori kii tulanaa querry bindu seey vibhajan tala taka kii sabse cumm doori seey karein. yeh uttarvarti doori yeh haye kii querry bindu aur nikatatam sambhaavit bindu key beach joe aadhe sthaan mein maujood hoe sakata haye, khoj naheen kii gaee. yadi yeh doori pahale key parinam mein vaapas kii gaee doori seey adhik haye, tou spasht roop seey dusare aadhe sthaan koo khojane kii koee aavashyakta naheen haye. yadi aisee aavashyakta haye, tou aapako dusare aadhe sthaan key liye samasya koo hull karane kii samasya seey gujarna hoga, aur phir isake parinam kii tulanaa poorv parinam seey karni hogi, aur phir uchit parinam lautana hoga. iss algorithm kaa pradarshan raikhik samay kii tulanaa mein logridmic samay key karib haye jaba querry bindu cloud key paas hotaa haye, kyonki querry bindu aur nikatatam bindu-cloud bindu key beach kii doori shoonya key karib hoti haye, isaliye algorithm koo kewal ack nazar daalane kii aavashyakta hoti haye taaki sahee parinam praapt karane key liye querry bindu kaa upayog kiya jaa sakey.
anuman vidhiyaan.
ack anumaanit nikatatam padosi khoj algorithm koo una binduon koo vaapas karane kii anumati haye jinaki doori querry seey querry seey usake nikatatam binduon taka kii doori kaa adhikatam sootra _ 1 gunaa haye. iss drishtikon kii appeal yeh haye kii, kaee mamalon mein, ack anumaanit nikatatam padosi lagbhag utanaa hii achchha haye jitna kii sateek. vishesh roop seey, yadi doori kaa maap upayogkarta kii gunavatta kii dhaarana koo sateek roop seey pakadata haye, tou doori mein chhote antar mayane naheen rakhate hain.
nikatata pados graph mein lalchi khoj.
nikatata graph vidhiyon (jaise kii aich. aine. aiss. doubleu.) koo anumaanit nikatatam padosiyon kii khoj key liye vartamaan atyaadhunik maanaa jaataa haye.
vidhiyaan nikatata key aalekhon key sootra 2 mein lalchi paar karane parr adharit hain jisamen pratyek bindu sootra 3 vishisht roop seey sheersh sootra 4 key saath judaa huaa haye. sett "s" mein ack prashn "q" key nikatatam padosiyon kii khoj graph sootra 2 mein sheersh key liye khoj kaa roop letee haye.
mool algorithm-lalchi khoj-nimnanusar kaam kartaa haih khoj ack pravishti-bindu sheersh sootra seey shuru hoti haye joe querry q seey usake pados sootra _ 7 key pratyek sheersh taka kii doori kii ganana karke shuru hoti haye, aur phir nyuntam doori moolya key saath ack sheersh paati haye. yadi querry aur chayanit sheersh key beach kii doori kaa maan prashn aur vartamaan tatva key beach kii doori seey chhota haye, tou algorithm chayanit sheersh parr chalaa jaataa haye, aur yeh nayaa pravesh-bindu bunn jaataa haye. algorithm taba rook jaataa haye jaba yeh sthaaniya nyuntam taka pahunch jaataa haih ack sheersh jisake pados mein ack sheersh naheen hotaa haye joe sheersh kii tulanaa mein prashn key karib hotaa haye.
nikatata pados graph key vichaar kaa kaee prakashanon mein upayog kiya gayaa thaa, jisamen aarya aur mount dwara mool kagaj, vimaan key liye voronet pranali mein, sootra _ 8 key liye rennet pranali mein, aur meterised chhoti duniya mein aur doori kaary key saath rikt sthaan key samanya mamle key liye aich. aine. aiss. doubleu. algorithm shamil hain. inn karyon seey pahale tossent dwara ack agrani pepper thaa, jisamen unhone "saapeksh pados" graph kii avadharana pesh kii thee.
sthaaniya samvedansheel hashing.
sthaaniya samvedansheel hashing (ell. aiss. aich.) sthaanon parr kuchh doori key metrick key aadhar parr 'baltiyon' mein sthaanon koo samoohbaddh karane kii ack takneek haye. chune gaye metrick key tahat ack dusare key karib honey vaale binduon koo uchch sambhavana key saath ack hii balty mein mapp kiya jaataa haye.
chhote aantarik ayam vaale sthaanon mein nikatatam padosi khoj.
aavaran vriksh kii ack saiddhaantik seema hoti haye joe dataset key dogune honey key sthiraank parr adharit hoti haye. khoj samay parr seema "oh" ("see" 12 logg "aine") haye jahan "see" dataset kaa vistaar sthiraank haye.
prakshepit radial khoj.
vishesh mamle mein jahaan detta jyaamitiya binduon kaa ack ghanaa 3 dee maanchitra haye, samvedan takneek kii prakshepan jyaamiti kaa upayog khoj samasya koo naatakiya roop seey saral banaane key liye kiya jaa sakata haye.
iss drishtikon key liye aavashyak haye kii 3dee detta koo ack dou-ayami grid key prakshepan dwara vyavasthit kiya jaae aur yeh maan liya jaae kii detta object seemaon key apavaad key saath padosi grid koshikaon mein sthaanik roop seey chikna haye.
yeye dhaaranaaen sarvekshan, robotics aur stereo drishti jaise anuprayogon mein 3dee samvedak detta key saath kaam karate samay maanya hoti hain, lekin samanya roop seey asangathit detta key liye naheen hoe sakati hain.
vyavhaar mein iss takneek mein vaastavik duniya key stereo drishti detta parr lagu honey parr "key"-nikatatam padosi samasya key liye "oh" ("1") yaa "oh" ("key") kaa ausat khoj samay hotaa haye.
vector sanniktan faailen.
uchch-ayami sthaanon mein, vriksh anukraman sanrachanaaen bekaar hoe jaati hain kyonki nodes key badhate pratishat kii vaise bhee jaanch karane kii aavashyakta hoti haye. raikhik khoj koo gati dene key liye, raim mein sangraheet feature vactor key ack sampeedit sanskaran kaa upayog pahale runn mein dataset koo poorv-filter karane key liye kiya jaataa haye. antim ummidvaaron koo dusare charan mein doori kii ganana key liye disk seey asankuchit detta kaa upayog karke nirdhaarit kiya jaataa haye.
sampeedan/clustering adharit khoj.
vaa-file drishtikon ack sampeedan adharit khoj kaa ack vishesh mamla haye, jahan pratyek visheshta ghatak koo samaan roop seey aur swatantra roop seey sampeedit kiya jaataa haye. bahuayami sthaanon mein ishtatam sampeedan takneek vector quantisation (vee. kyu.) haye, jise clustering key madhyam seey lagu kiya jaataa haye. databases samoohbaddh haye aur sabse "ashajanak" samoohon koo punarpraapt kiya jaataa haye. vaa-file, vriksh-adharit soochkaank aur anukramik scan parr bhaari laabh dekhaa gayaa haye. clustering aur ell. aiss. aich. key beach samaantaon koo bhee nott karein.
roop.
aine. aine. aiss. samasya key kaee roop hain aur dou sabse prasiddh hain "key"-nikatatam padosi khoj aur ε-nikatatam padosi khoj.
"key"-nikatatam padosi.
"key"-nikatatam padosi khoj querry key sheersh "key" nikatatam padosiyon kii pehchaan karati haye. iss takneek kaa upayog aamtaur parr bhavishyasoochak vishleshan mein apane padosiyon kii aam sahamati key aadhar parr ack bindu kaa anuman lagaane yaa vargeekrit karane key liye kiya jaataa haye. "key"-nikatatam padosi graph graph hain jinamen pratyek bindu apane nikatatam padosiyon seey judaa hotaa haye.
lagbhag nikatatam padosi.
kuchh anuprayogon mein nikatatam padosi kaa "achchha anuman" nikaalana sweekarya hoe sakata haye. una mamalon mein, humm ack algorithm kaa upayog curr sakate hain joe behtar gati yaa smriti bachat key badale mein harr mamle mein vaastavik nikatatam padosi koo vaapas karane kii guaranti naheen detaa haye. aksar iss tarah key ack algorithm koo adhikansh mamalon mein nikatatam padosi milega, lekin yeh dridhata seey dataset seey poochtaachh parr nirbhar kartaa haye.
lagbhag nikatatam padosi khoj kaa samarthan karane vaale algorithm mein sthaaniya-samvedansheel hashing, sabse achchha binn pratham aur santulit boxes-apghatan vriksh adharit khoj shamil hain.
nikatatam padosi doori anupaat.
nikatatam padosi doori anupaat mool bindu seey pratidvandi padosi taka kii seedhi doori parr seema lagu naheen kartaa haye, balki pichhale padosi seey doori key aadhar parr isake anupaat parr lagu hotaa haye. iska upayog sthaaniya visheshtaon key beach samaantaa kaa upayog karke "udaaharan dwara prashn" key madhyam seey chitron koo praapt karane key liye see. bee. aar. mein kiya jaataa haye. adhik aam taur parr yeh kaee milan samasyaon mein shamil haye.
padosiyon key paas nishchit trijya.
padosiyon key paas nishchit-trijya vaha samasya haye jahan koee ack nirdisht bindu seey dee gaee nishchit doori key bheetar euclidean sthaan mein diye gaye sabhi binduon koo kushalata seey khojana chaahata haye. doori taya maani jaati haye, lekin prashn bindu manmana haye.
sabhi nikatatam padosi.
kuchh anuprayogon key liye (ee.jee. entropy anuman), hamaare paas "aine" detta-bindu hoe sakate hain aur humm jaanana chaahte hain kii una aine binduon mein seey pratyek key liye nikatatam padosi kaun saa haye. yeh, nishchit roop seey, harr bindu key liye ack baar nikatatam-padosi khoj chalaakar praapt kiya jaa sakata haye, lekin ack behtar ranneeti ack algorithm hogi joe inn "aine" prashnon key beach jaankaari atirek kaa dohan karati haye taaki adhik kushal khoj kaa utpaadan kiya jaa sakey. ack saral udaaharan key roop menh jaba humm bindu "x" seey bindu "y" taka kii doori paate hain, tou yeh hamein bindu "y" seey bindu "x" taka kii doori bhee bataata haye, isaliye ack hii ganana kaa dou alag-alag prashnon mein punah upayog kiya jaa sakata haye.
ack nishchit ayam, ack ardh-nishchit sakaratmak maanak (jisase pratyek ell. pee. maanak sahit), aur iss sthaan mein "aine" bindu diye gaye hain, pratyek bindu kaa nikatatam padosi "oh" ("aine" logg "aine") samay mein paaya jaa sakata haye aur pratyek bindu key "aim" nikatatam padosi "oh" ("mn" logg "aine") samay mein paae jaa sakate hain.

