Intshayelelo yokuXhomekeka koMsebenzi

Kweli nqaku siza kuthetha ngokuxhomekeka okusebenzayo kwiinkcukacha zolwazi - ukuba ziphi, apho zisetyenziswa khona kwaye zeziphi ii-algorithms ezikhoyo ukuze zifumaneke.

Siza kuqwalasela ukuxhomekeka okusebenzayo kumxholo wolwazi olunxulumeneyo. Ukuyibeka ngokurhabaxa kakhulu, kwezo nkcukacha zolwazi zigcinwa ngohlobo lweetafile. Okulandelayo, sisebenzisa iikhonsepthi eziqikelelweyo ezingatshintshiyo kwithiyori engqongqo yobudlelwane: siya kuyibiza itafile ngokwayo njengolwalamano, iikholamu - iimpawu (iseti yazo - i-schema yobudlelwane), kunye neseti yamaxabiso omqolo kwi-subset yeempawu. - i-tuple.

Umzekelo, kule theyibhile ingentla, (UBenson, M, M organ) liqela leempawu (Isigulane, uPawulos, uGqirha).
Ngokusesikweni ngakumbi, oku kubhalwe ngolu hlobo lulandelayo: [Isigulana, isini, uGqirha] = (uBenson, M, M organ).
Ngoku sinokwazisa ingqikelelo yokuxhomekeka kokusebenza (FD):

Inkcazo 1. Unxulumano R lwanelisa umthetho womanyano X → Y (apho X, Y ⊆ R) ukuba kwaye kuphela ukuba kuzo naziphi na ii-tuples , ∈ R ubamba: ukuba [X] = [X], ngoko [Y] = [Y]. Kule meko, sithi u-X (i-determinant, okanye isethi echazayo yeempawu) imisela ngokusebenzayo u-Y (isethi exhomekeke kuyo).

Ngamanye amazwi, ubukho bomthetho wobumbano X → Y kuthetha ukuba ukuba sinee-tuples ezimbini R kwaye ziyahambelana ngeempawu X, emva koko ziya kuhambelana kwiimpawu Y.
Kwaye ngoku, ngolungelelwano. Makhe sijonge iimpawu Umonde и Ngesondo apho sifuna ukufumanisa ukuba kukho ukuxhomekeka phakathi kwabo okanye hayi. Kwiseti yeempawu ezinjalo, oku kuxhomekeka kulandelayo kunokubakho:

1. Isigulana → Isini
2. Isini → Isigulane

Njengoko kuchaziwe ngasentla, ukuze ukuxhomekeka kokuqala kubambe, ixabiso ngalinye lekholamu eyodwa Umonde ixabiso lekholamu enye kuphela elimele lihambelane Ngesondo. Kwaye kwitheyibhile yomzekelo oku kunjalo ngokwenene. Nangona kunjalo, oku akusebenzi kwicala elichaseneyo, oko kukuthi, ukuxhomekeka okwesibini akwanelanga, kunye nophawu. Ngesondo ayisisimiseli se Umonde. Ngokufanayo, ukuba sithatha ukuxhomekeka Ugqirha → Isigulana, unokubona ukuba yaphulwa, ekubeni ixabiso URobin olu phawu luneentsingiselo ezininzi ezahlukeneyo - uEllis kunye noGraham.

Ngaloo ndlela, ukuxhomekeka okusebenzayo kwenza kube lula ukumisela ubudlelwane obukhoyo phakathi kweeseti zeempawu zetafile. Ukusuka apha ukuya phambili siya kuqwalasela olona nxibelelwano lunomdla, okanye kunoko lunjalo X → Yyintoni abayiyo:

• non-trivial, oko kukuthi, icala lasekunene lokuxhomekeka aliyiyo i-subset yekhohlo (Y ̸⊆ X);
• ubuncinci, oko kukuthi, akukho kuxhomekeka okunjalo Z → Y, oko Z ⊂ X.

Ukuxhomekeka kuqwalaselwe ukuza kuthi ga kweli nqanaba kwakungqongqo, oko kukuthi, abazange babonelele naluphi na ukuphulwa kwetafile, kodwa ukongeza kubo, kukho nabo bavumela ukungahambelani phakathi kwemilinganiselo yee-tuples. Ukuxhomekeka okunjalo kufakwe kwiklasi eyahlukileyo, ebizwa ngokuba yi-approximate, kwaye kuvunyelwe ukuphulwa kwinani elithile lee-tuples. Esi sixa-mali silawulwa ngowona mqondiso wemposiso enkulu emax. Umzekelo, izinga lempazamo = I-0.01 inokuthetha ukuba ukuxhomekeka kunokuphulwa nge-1% yee-tuples ezikhoyo kwisethi yeempawu ezicatshangelwayo. Oko kukuthi, kwiirekhodi ze-1000, ubuninzi bee-tuples ze-10 zingaphula uMthetho we-Federal. Siza kuthathela ingqalelo i-metric eyahluke kancinci, esekwe kumaxabiso ahlukeneyo ahlukeneyo ee-tuples ezithelekisayo. Kuba likhoboka X → Y kwisimo sengqondo r ithathwa ngolu hlobo:

Masibale impazamo ye Ugqirha → Isigulana kumzekelo ongasentla. Sinee-tuples ezimbini ezinexabiso elahlukileyo kuphawu Umonde, kodwa zihambelana Gqirha: [Gqirha, isigulane] = (URobin, uEllis) kunye [Gqirha, isigulane] = (URobin, uGraham). Ukulandela inkcazo yempazamo, kufuneka sithathele ingqalelo zonke izibini eziphikisanayo, okuthetha ukuba kuya kubakho ezimbini zazo: (, ) kunye nokuguqulwa kwayo (, ). Masiyitshintshe kwifomula kwaye sifumane:

Ngoku makhe sizame ukuphendula lo mbuzo: "Kutheni yonke le nto?" Enyanisweni, imithetho ye-federal yahlukile. Uhlobo lokuqala lwezo zixhomekeke ezichazwe ngumlawuli kwinqanaba loyilo lwedatha. Ngokuqhelekileyo bambalwa ngenani, bangqongqo, kwaye usetyenziso oluphambili luhlengahlengiso lwedatha kunye noyilo lweschema sobudlelwane.

Uhlobo lwesibini luxhomekeke, olumele idatha "efihliweyo" kunye nobudlelwane obungaziwa ngaphambili phakathi kweempawu. Okokuthi, ukuxhomekeka okunjalo akuzange kucatshangelwe ngexesha loyilo kwaye zifunyenwe kwiseti yedatha ekhoyo, ukwenzela ukuba kamva, ngokusekelwe kwimithetho emininzi echongiweyo ye-federal, naziphi na izigqibo ezinokuthi zenziwe malunga nolwazi olugciniweyo. Koku kuxhomekeke kanye esisebenza kunye nabo. Bajongana nayo yonke intsimi yeemayini zedatha ngeendlela ezahlukeneyo zokukhangela kunye ne-algorithms eyakhelwe kwisiseko sabo. Makhe sibone indlela ukuxhomekeka okufunyenweyo okusebenzayo (okuchanekileyo okanye kuqikelelo) kuyo nayiphi na idatha kunokuba luncedo.

Namhlanje, enye yezicelo eziphambili zokuxhomekeka kukucoca idatha. Kubandakanya ukuphuhlisa iinkqubo zokuchonga "idatha engcolileyo" kwaye emva koko uyilungise. Imizekelo ebalaseleyo "yedatha emdaka" yimpinda, iimpazamo zedatha okanye ii-typos, amaxabiso alahlekileyo, idatha ephelelwe lixesha, izithuba ezongezelelweyo, nokunye okunjalo.

Umzekelo wempazamo yedatha:

Umzekelo wokuphindwa kwedatha:

Umzekelo, sinetafile kunye neseti yemithetho ye-federal ekufuneka iphunyezwe. Ukucocwa kwedatha kule meko kubandakanya ukutshintsha idatha ukuze iMithetho ye-Federal ibe ichanekile. Kule meko, inani lokuguqulwa kufuneka libe lincinci (le nkqubo ine-algorithms yayo, esingayi kugxila kuyo kweli nqaku). Ngezantsi umzekelo wenguqu yedatha enjalo. Ngasekhohlo ubudlelwane bokuqala, apho, ngokucacileyo, ii-FL eziyimfuneko azihlangabezwanga (umzekelo wokuphulwa kwesinye se-FL ugxininiswe ebomvu). Ekunene lubudlelwane obuhlaziyiweyo, kunye neeseli eziluhlaza ezibonisa amaxabiso atshintshileyo. Emva kwale nkqubo, ukuxhomekeka okuyimfuneko kwaqala ukugcinwa.

Esinye isicelo esidumileyo kuyilo lwedatha. Apha kuyafaneleka ukukhumbula iifom eziqhelekileyo kunye nokuqhelekileyo. I-normalization yinkqubo yokuzisa ubudlelwane ngokuhambelana neseti ethile yeemfuno, nganye kuzo ichazwa ngendlela eqhelekileyo ngendlela yayo. Asiyi kuchaza iimfuno zeefom ezahlukeneyo eziqhelekileyo (oku kwenziwa kuyo nayiphi na incwadi kwikhosi yedatha yabaqalayo), kodwa siya kuqaphela kuphela ukuba ngamnye wabo usebenzisa ingcamango yokuxhomekeka komsebenzi ngendlela yayo. Emva kwayo yonke loo nto, iiFLs ziyimiqobo yengqibelelo yendalo ethathelwa ingqalelo xa kuyilwa isiseko sedatha (kwimeko yalo msebenzi, iiFL ngamanye amaxesha zibizwa ngokuba zii-superkeys).

Makhe siqwalasele isicelo sabo kwiifom ezine eziqhelekileyo kulo mfanekiso ungezantsi. Khumbula ukuba ifom ye-Boyce-Codd yesiqhelo ingqongqo ngakumbi kuneyesithathu, kodwa ingaphantsi kweyesine. Asiyi kuqwalasela okokugqibela ngoku, ekubeni ukuqulunqwa kwayo kufuna ukuqonda ukuxhomekeka kwamanani amaninzi, okungathandekiyo kuthi kweli nqaku.

Omnye ummandla apho abantu abaxhomekeke kuye bafumene isicelo sabo kukunciphisa ubungakanani bendawo yophawu kwimisebenzi efana nokwakha umdidi weBayes ongenalwazi, ukuchonga iimpawu ezibalulekileyo, kunye nokuhlaziya kwakhona imodeli yokubuyisela umva. Kumanqaku asekuqaleni, lo msebenzi ubizwa ngokuba kukumiselwa kokungafunekiyo kunye nokufaneleka kweempawu [5, 6], kwaye isonjululwe ngokusetyenziswa okusebenzayo kweengqikelelo zedatha. Ngokufika kwemisebenzi enjalo, sinokuthi namhlanje kukho imfuno yezisombululo ezivumela ukuba sidibanise i-database, i-analytics kunye nokuphunyezwa kweengxaki ezingentla apha kwisixhobo esinye [7, 8, 9].

Kukho iindlela ezininzi zokuziphatha (zombini zangoku kwaye azikho zangoku) zokukhangela imithetho yobumbano kwiseti yedatha.

• I-algorithms kusetyenziswa ukunqunyulwa kweelethi zealgebra (i-Lattice traversal algorithms)
• Ii-algorithms ezisekwe kuphendlo lwamaxabiso ekuvunyelwene ngawo (Umahluko- kunye nokuvumelana-sete algorithms)
• Ii-algorithms ezisekwe kuthelekiso lwe-pairwise (I-algorithms yokwenziwa kokuxhomekeka)

Inkcazo emfutshane yohlobo ngalunye lwe-algorithm inikwe kwitheyibhile engezantsi:


Unokufunda ngakumbi ngolu hlelo [4]. Ngezantsi yimizekelo ye-algorithms kudidi ngalunye:

Okwangoku, kuvela ii-algorithms ezintsha ezidibanisa iindlela ezininzi zokufumana ukuxhomekeka kokusebenza. Imizekelo yaloo migaqo yiPyro [2] kunye neHyFD [3]. Uhlalutyo lomsebenzi wabo lulindelwe kumanqaku alandelayo olu ngcelele. Kweli nqaku, siza kuphonononga kuphela iikhonsepthi ezisisiseko kunye ne-lemma eziyimfuneko ukuze siqonde iindlela zokufumanisa ukuxhomekeka.

Masiqale ngolunye olulula - umahluko- kwaye uvumelane-seti, esetyenziswe kudidi lwesibini lwe-algorithms. Umahluko-iseti liqela leekopi ezingenamaxabiso afanayo, ngelixa i- agree-set, ngokuchaseneyo, zii tuples ezinexabiso elifanayo. Kuyafaneleka ukuba uqaphele ukuba kule meko siqwalasela kuphela icala lasekhohlo lokuxhomekeka.

Enye ingcamango ebalulekileyo ekuye kwahlangatyezwana nayo ngasentla yilathisi yealgebra. Kuba ii-algorithms ezininzi zanamhlanje zisebenza kule ngcamango, kufuneka sibe nombono wokuba yintoni na.

Ukuze uqalise ingqikelelo yeletisi, kuyimfuneko ukuchaza isethi ecwangcisiweyo ngokuyinxenye (okanye isethi eyakhiwe ngokuyinxenye, ifinyeziwe njenge-poset).

Inkcazo 2. Isethi S kuthiwa iodolwa ngokuyinxenye ngonxulumano lokubini ⩽ ukuba kuzo zonke a, b, c ∈ S ezi mpawu zilandelayo zanelisiwe:

1. Reflexivity, oko kukuthi, a ⩽ a
2. Antisymmetry, oko kukuthi, ukuba ⩽ b kunye no b ⩽ a, emva koko a = b
3. Utshintsho, oko kukuthi, ku ⩽ b kunye no b ⩽ c kulandela ukuba a ⩽ c

Unxulumano olunjalo lubizwa ngokuba lunxulumano lomyalelo (oluxekileyo) oluyinxenye, kwaye iseti ngokwayo ibizwa ngokuba luseti olucwangcisiweyo. Ubhalo olusesikweni: ⟨S, ⩽⟩.

Njengowona mzekelo ulula weseti eodolwe ngokuyinxenye, singathatha isethi yawo onke amanani endalo N ngonxulumano oluqhelekileyo lolandelelwano ⩽. Kulula ukuqinisekisa ukuba zonke ii-axiom eziyimfuneko zanelisiwe.

Umzekelo onentsingiselo ngakumbi. Qwalasela iseti yazo zonke iiseti ezisezantsi {1, 2, 3}, zicwangciswe ngonxulumano lokuqukwa ⊆. Ngokwenene, olu nxulumano lwanelisa zonke iimeko zocwangco, ngoko ke ⟨P ({1, 2, 3}), ⊆⟩ yiseti ecwangcisiweyo. Lo mzobo ungezantsi ubonisa ubume beli seti: ukuba into enye inokufikelelwa ngeentolo ukuya kwenye into, ngoko ke bakubudlelwane bomyalelo.

Siya kufuna iingcaciso ezimbini ezilula ngakumbi kwicandelo lemathematika - supremum kunye ne-infimum.

Inkcazo 3. Mayibe ⟨S, ⩽⟩ ibe lucwangciswe ngokuyinxenye, A ⊆ S. Umda ophezulu ka-A sisiqalelo u ∈ S ukuze ∀x ∈ S: x ⩽ u. Mayibe ngu-U iseti yayo yonke imida ephezulu ka-S. Ukuba kukho eyona elementi incinci ku-U, ngoko ibizwa ngokuba yi-supremum kwaye ichazwa njenge-sup A.

Ingqikelelo yomda osezantsi ngokuthe ngqo yaziswa ngokufanayo.

Inkcazo 4. Mayibe ⟨S, ⩽⟩ ibe yiseti eodolwe ngokuyinxenye, A ⊆ S. I-infimum ka-A sisiqalelo u-l ∈ S ukuze ∀x ∈ S: l ⩽ x. Mayibe ngu L ibe yiseti yayo yonke imida esezantsi ka S. Ukuba kukho eyona elementi inkulu ku L, ke ibizwa ngokuba yi infimum kwaye ichazwa njenge inf A.

Qwalasela njengomzekelo le iseti eodolwe ngokuyinxenye ingentla ⟨P ({1, 2, 3}), ⊆⟩ kwaye ufumane i-supremum kunye ne-infimum kuyo:

Ngoku sinokuqulunqa inkcazo ye-algebraic lattice.

Inkcazo 5. Vumela i-⟨P,⩽⟩ ibe lucwangciswe ngokuyinxenye oluyalelwe ukuba isiqalelo ngasinye seseti esezantsi ibe nomda ophezulu nasezantsi. Emva koko u-P ubizwa ngokuba yi-algebraic lattice. Kule meko, sup{x, y} ibhalwe njenge x ∨ y, kunye ne-inf {x, y} njenge-x ∧ y.

Masijonge ukuba umzekelo wethu osebenzayo ⟨P ({1, 2, 3}), ⊆⟩ yilathisi. Ngokwenene, kuyo nayiphi na i-a, b ∈ P ({1, 2, 3}), a∨b = a∪b, kunye no-a∧b = a∩b. Umzekelo, qwalasela iiseti {1, 2} kunye {1, 3} kwaye ufumane i-infimum kunye ne-supremum yazo. Ukuba siyazinqumla, siya kufumana isethi {1}, eya kuba yi-infimum. Sifumana i-supremum ngokudibanisa - {1, 2, 3}.

Kwi-algorithms yokuchonga iingxaki zomzimba, indawo yokukhangela idla ngokumelwa ngendlela yeletisi, apho iiseti zento enye (funda inqanaba lokuqala leleti yokukhangela, apho icala lasekhohlo labaxhomekeke liqulathe uphawu olunye) limele uphawu ngalunye. yobudlelwane bokuqala.
Okokuqala, siqwalasela ukuxhomekeka kwifom ∅ → Uphawu olunye. Eli nyathelo likuvumela ukuba ugqibezele ukuba zeziphi iimpawu ezizizitshixo eziphambili (kwiimpawu ezinjalo azikho izichazi, kwaye ke icala lasekhohlo alinanto). Ngapha koko, i-algorithms enjalo ihambela phezulu kunye ne-lattice. Kuyafaneleka ukuba uqaphele ukuba akuyiyo yonke i-lattice enokuthi igqitywe, oko kukuthi, ukuba ubungakanani obunqwenelekayo becala lasekhohlo bugqithiselwe kwigalelo, ngoko i-algorithm ayiyi kuhamba ngaphezu kwenqanaba kunye nobukhulu.

Umfanekiso ongezantsi ubonisa indlela i-algebraic lattice enokusetyenziswa ngayo kwingxaki yokufumana i-FZ. Nanku umphetho ngamnye (X, XY) imele ukuxhomekeka X → Y. Umzekelo, siphumelele inqanaba lokuqala kwaye siyazi ukuba umlutha ugcinwa A → B (siya kubonisa oku njengodibaniso oluluhlaza phakathi kwee-vertices A и B). Oku kuthetha ukuba ngokubhekele phaya, xa sinyuka ecaleni kweletisi, asinakukhangela ukuxhomekeka A, C → B, kuba ayisayi kuba ncinane. Ngokufanayo, asizukuyijonga ukuba ukuxhomekeka kubanjwe C → B.

Ukongeza, njengomthetho, zonke ii-algorithms zanamhlanje zokukhangela imithetho ye-federal zisebenzisa ulwakhiwo lwedatha olufana nolwahlulo (kwimvelaphi yoqobo - isahlulelo esihluthiweyo [1]). Inkcazo esesikweni yolwahlulo ngolu hlobo lulandelayo:

Inkcazo 6. Vumela u-X ⊆ R abe liqela leempawu zonxulumano r. Iqela yiseti yezalathisi ze tuples kwi r ezinexabiso elifanayo ku X, oko kukuthi, c(t) = {i|ti[X] = t[X]}. Isahlulo yiseti yamaqela, ngaphandle kwezihloko zobude beyunithi:

Ngamagama alula, isahlulelo sophawu X yiseti yoluhlu, apho uluhlu ngalunye luqulathe amanani elayini anamaxabiso afanayo e X. Kuncwadi lwangoku, isakhiwo esimele izahlulelo sibizwa ngokuba yi-position list index (PLI). Amaqela obude beyunithi awabandakanywa kwiinjongo zokunyanzeliswa kwe-PLI kuba ngamaqela aqulethe kuphela inombolo yerekhodi enexabiso elikhethekileyo eliya kuhlala lilula ukulichonga.

Makhe sijonge umzekelo. Masibuyele kwitafile enye kunye nezigulane kwaye sakhe izahlulo zeekholomu Umonde и Ngesondo (umhlathi omtsha uvele ekhohlo, apho amanani omqolo wetafile aphawulwe):

Ngaphezu koko, ngokwenkcazo, ulwahlulo lwekholamu Umonde ngenene izakuhlala ingenanto, kuba amaqela omnye akaqukwanga kwisahlulelo.

Izahlulo zinokufunyanwa ngeempawu ezininzi. Kwaye kukho iindlela ezimbini zokwenza oku: ngokuhamba ngetafile, yakha isahlulo usebenzisa zonke iimpawu eziyimfuneko ngexesha elinye, okanye uyakhe usebenzisa i-intersection ye-partitions usebenzisa i-subset yeempawu. Umthetho we-Federal search algorithms usebenzisa inketho yesibini.

Ngamagama alula, ukuya, umzekelo, ukufumana isahlulelo ngamakholomu ABC, ungathatha izahlulo ze AC и B (okanye nayiphi na enye iseti yeeseti ezidityanisiweyo) kwaye zinqumle enye kwenye. Ukusebenza kwesiphambano sezahlulo ezibini ukhetha amaqoqo obude obuninzi obuqhelekileyo kuzo zombini izahlulo.

Makhe sijonge umzekelo:

Kwimeko yokuqala, safumana isahlulelo esingenanto. Ukuba ujonga ngokusondeleyo etafileni, ke ngokwenene, akukho maxabiso afanayo kwezi mpawu zimbini. Ukuba siguqula kancinane itafile (ityala ngasekunene), siya kuba sele sifumana isiphambuka esingenanto. Ngapha koko, umgca 1 kunye no-2 eneneni unamaxabiso afanayo eempawu Ngesondo и Ugqirha.

Okulandelayo, siya kufuna ingcamango efana nobukhulu besahlulelo. Ngokusesikweni:

Ukubeka ngokulula, ubungakanani besahlulelo linani leqela elibandakanyiweyo kwisahlulelo (khumbula ukuba iqoqo elinye aliqukwanga kwisahlulelo!):

Ngoku sinokuchaza enye ye-lemmas engundoqo, ethi izahlulo ezinikiweyo zisivumele ukuba sigqibe ukuba ukuxhomekeka kubanjwe okanye akunjalo:

Lemma 1. Ukuxhomekeka A, B → C kubamba ukuba kwaye kuphela ukuba

Ngokwe-lemma, ukufumanisa ukuba ukuxhomekeka kubambe, amanyathelo amane kufuneka enziwe:

1. Bala isahlulo secala lasekhohlo lokuxhomekeka
2. Bala isahlulelo kwicala lasekunene lokuxhomekeka
3. Bala imveliso yenyathelo lokuqala nelesibini
4. Thelekisa ubungakanani bezahlulo ezifunyenwe kwinqanaba lokuqala nelesithathu

Apha ngezantsi ngumzekelo wokukhangela ukuba ngaba ukuxhomekeka kubambe ngokwale lemma:

Kweli nqaku, sihlolisise iikhonsepthi ezifana nokuxhomekeka kokusebenza, ukuxhomekeka kokusebenza okusondeleyo, kujongwe apho zisetyenziselwa khona, kunye nokuba yeyiphi i-algorithms yokukhangela imisebenzi yomzimba ekhoyo. Siphinde saphonononga ngokweenkcukacha iikhonsepthi ezisisiseko kodwa ezibalulekileyo ezisetyenziswa ngokusebenzayo kwii-algorithms zanamhlanje zokukhangela imithetho yomanyano.

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Ababhali beli nqaku: UAnastasia Birillo, umphandi kwi Uphando lweJetBrains, Umfundi weziko le-CS и UNikita Bobrov, umphandi kwi Uphando lweJetBrains

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