Kulesi sihloko sizokhuluma ngokuncika kokusebenza kuzinqolobane zolwazi - ukuthi ziyini, zisetshenziswa kuphi nokuthi yimaphi ama-algorithms akhona ukuze uwathole.
Sizocubungula ukuncika kokusebenza kumongo wolwazi olugciniwe. Ukukubeka kancane, kulwazi olunjalo lugcinwa ngendlela yamathebula. Okulandelayo, sisebenzisa imiqondo elinganiselwe engaguquguquki emcabangweni oqinile wobudlelwano: sizobiza ithebula ngokwalo ubudlelwano, amakholomu - izimfanelo (isethi yawo - i-schema yobudlelwano), kanye nesethi yamanani emigqa kusethi yezimfanelo. - i-tuple.
Isibonelo, kuthebula elingenhla, (Benson, M, M isitho) isiqephu sezici (Isiguli, uPaul, udokotela).
Ngokusemthethweni, lokhu kubhalwe kanje: [Isiguli, Ubulili, Udokotela] = (Benson, M, M organ).
Manje sesingathula umqondo wokuthembela kokusebenza (FD):
Incazelo 1. Ubudlelwano R banelisa umthetho wenhlangano X → Y (lapho u-X, Y ⊆ R) uma futhi kuphela uma kungama-tuples , ∈ R ubamba: uma [X] = [X], bese [Y] = [Y]. Kulokhu, sithi u-X (i-determinant, noma isethi echazayo yezici) inquma ngokusebenzayo u-Y (isethi encikile).
Ngamanye amazwi, ukuba khona komthetho we-federal X → Y kusho ukuthi uma sinama-tuples amabili phakathi R futhi ziyahambelana ngezici X, khona-ke zizoqondana ngezimfanelo Y.
Futhi manje, ngokulandelana. Ake sibheke izimfanelo Isiguli и Ubulili esifuna ukuthola ukuthi kukhona ukuncika phakathi kwabo noma cha. Kusethi yezibaluli ezinjalo, kungase kube khona ukuncika okulandelayo:
- Isiguli → Ubulili
- Ubulili → Isiguli
Njengoba kuchazwe ngenhla, ukuze kubambe ukuncika kokuqala, inani lekholomu ngalinye eliyingqayizivele Isiguli inani lekholomu elilodwa kuphela okufanele lifane Ubulili. Futhi kuthebula lesibonelo lokhu kunjalo ngempela. Kodwa-ke, lokhu akusebenzi ngokuphambene, okungukuthi, ukuncika kwesibili akunelisekile, futhi imfanelo Ubulili akusona isinqumo salokhu Isiguli. Ngokufanayo, uma sithatha ukuncika Udokotela → Isiguli, uyabona ukuthi iphuliwe, kusukela inani Robin lesi sici sinezincazelo eziningana ezahlukene - Ellis kanye no Graham.
Ngakho, ukuncika kokusebenza kwenza kube nokwenzeka ukunquma ubudlelwano obukhona phakathi kwamasethi ezibaluli zethebula. Kusukela lapha kuya phambili sizocubungula ukuxhumana okuthakazelisa kakhulu, noma kunalokho X → Ylokho abayikho:
- okungeyona into encane, okungukuthi, uhlangothi lwesokudla lokuncika aluyona isethi engaphansi kwesokunxele (Y ̸⊆ X);
- okuncane, okungukuthi, akukho ukuncika okunjalo Z → Y, lokho Z ⊂ X.
Ukuncika okucatshangelwe kuze kube kuleli phuzu kwakuqinile, okungukuthi, akuzange kunikeze noma yikuphi ukwephulwa kwetafula, kodwa ngaphezu kwabo, kukhona nalabo abavumela ukungqubuzana okuthile phakathi kwamanani we-tuples. Ukuncika okunjalo kubekwa ekilasini elihlukile, elibizwa ngokuthi isilinganiso, futhi kuvunyelwe ukuba kwephulwe ngenani elithile lama-tuples. Leli nani lilawulwa ubukhulu benkomba yephutha emax. Isibonelo, izinga lephutha = 0.01 kungase kusho ukuthi ukuncika kungaphulwa ngo-1% wama-tuples atholakalayo kusethi ecatshangelwayo yezibaluli. Okusho ukuthi, kumarekhodi ayi-1000, inani eliphakeme lama-tuples ayi-10 lingaphula uMthetho Wombuso. Sizocubungula imethrikhi ehluke kancane, esekelwe kumanani ahlukene ahlukene ngokubili wama-tuples aqhathaniswayo. Ukuze umlutha X → Y ngesimo sengqondo r kubhekwa kanje:
Ake sibale iphutha Udokotela → Isiguli kusukela esibonelweni esingenhla. Sinama-tuples amabili amanani awo ahluka kusibaluli Isiguli, kodwa kuhambisane Udokotela: [Udokotela, Isiguli] = (Robin, Ellis) futhi [Udokotela, Isiguli] = (Robin, Graham). Ukulandela incazelo yephutha, kufanele sicabangele wonke amapheya ashayisanayo, okusho ukuthi kuzoba nokubili kwawo: (, ) kanye nokuguqulwa kwayo (, ). Masiyishintshe kufomula futhi sithole:
Manje ake sizame ukuphendula lo mbuzo: "Kungani konke lokhu?" Eqinisweni, imithetho ye-federal ihlukile. Uhlobo lokuqala yilabo abancikile abanqunywa umlawuli esigabeni sokuklama sesizindalwazi. Ngokuvamile zimbalwa ngenani, ziqinile, futhi uhlelo lokusebenza oluyinhloko ukujwayela kwedatha kanye nokwakhiwa kwe-schema esihlobene.
Uhlobo lwesibili ukuncika, olumelela idatha "efihliwe" kanye nobudlelwano obungaziwa ngaphambili phakathi kwezici. Okungukuthi, ukuncika okunjalo akuzange kucatshangelwe ngesikhathi sokuklama futhi kutholakala kusethi yedatha ekhona, ukuze kamuva, ngokusekelwe emithethweni eminingi ye-federal ekhonjiwe, noma yiziphi iziphetho zingathathwa mayelana nolwazi olugciniwe. Yilokhu kuncika impela esisebenza ngakho. Kubhekwana nayo yonke insimu yokumbiwa kwedatha ngamasu okusesha ahlukahlukene kanye nama-algorithms akhelwe phezu kwesisekelo sawo. Ake sithole ukuthi ukuncika okutholakele okusebenzayo (okuqondile noma okulinganiselwe) kunoma iyiphi idatha kungaba usizo.
Namuhla, enye yezinhlelo zokusebenza eziyinhloko zokuncika ukuhlanza idatha. Kubandakanya ukuthuthukisa izinqubo zokuhlonza "idatha engcolile" bese uyayilungisa. Izibonelo ezivelele "zedatha engcolile" ziyimpinda, amaphutha edatha noma ama-typos, amanani ashodayo, idatha ephelelwe yisikhathi, izikhala ezengeziwe, nokunye okunjalo.
Isibonelo sephutha ledatha:
Isibonelo sezimpinda kudatha:
Isibonelo, sinethebula nesethi yemithetho yenhlangano okufanele ilandelwe. Ukuhlanza idatha kuleli cala kuhilela ukushintsha idatha ukuze i-Federal Laws ibe elungile. Kulokhu, inani lokuguqulwa kufanele libe lincane (le nqubo ine-algorithms yayo, esingeke sigxile kuyo kulesi sihloko). Ngezansi isibonelo sokuguqulwa kwedatha enjalo. Ngakwesobunxele kukhona ubuhlobo bokuqala, lapho, ngokusobala, ama-FL adingekayo angafinyelelwanga (isibonelo sokuphulwa kwesinye se-FL sigqanyiswe ngokubomvu). Kwesokudla ubudlelwano obubuyekeziwe, namaseli aluhlaza abonisa amanani ashintshile. Ngemuva kwale nqubo, ukuncika okudingekayo kwaqala ukugcinwa.
Olunye uhlelo lokusebenza oludumile ukuklama kwedatha. Lapha kufanelekile ukukhumbula amafomu ajwayelekile kanye nokujwayelekile. Ukujwayela kuyinqubo yokuletha ubudlelwano ekuhambisaneni nesethi ethile yezidingo, ngayinye yazo echazwa ngendlela evamile ngendlela yayo. Ngeke sichaze izidingo zamafomu ahlukahlukene ajwayelekile (lokhu kwenziwa kunoma iyiphi incwadi esifundweni sesizindalwazi sabaqalayo), kodwa sizoqaphela kuphela ukuthi ngamunye wabo usebenzisa umqondo wokuncika kokusebenza ngendlela yakhe. Phela, ama-FL ayizithiyo ngokwemvelo zobuqotho ezicatshangelwa lapho kwakhiwa isizindalwazi (ngokwengqikithi yalo msebenzi, ama-FL ngezinye izikhathi abizwa ngokuthi okhiye abakhulu).
Ake sicabangele isicelo sabo samafomu amane ajwayelekile esithombeni esingezansi. Khumbula ukuthi ifomu elivamile lika-Boyce-Codd liqinile kunefomu lesithathu, kodwa aliqinile kunelesine. Asicabangi lokhu okwakamuva okwamanje, njengoba ukwakheka kwayo kudinga ukuqonda kokuncika okunenani eliningi, okungasithakazelisi kulesi sihloko.
Enye indawo lapho ukuncika kuthole khona uhlelo lwakho lokusebenza ukunciphisa ubukhulu besikhala sesici emisebenzini efana nokwakha isigaba se-Bayes esingazi lutho, ukuhlonza izici ezibalulekile, nokwenza kabusha imodeli yokuhlehla. Ezihlokweni zokuqala, lo msebenzi ubizwa ngokuthi ukunqunywa kokungafuneki kanye nokuhambisana kwesici [5, 6], futhi uxazululwa ngokusetshenziswa okusebenzayo kwemiqondo yesizindalwazi. Ngokufika kwemisebenzi enjalo, singasho ukuthi namuhla kunesidingo sezixazululo ezisivumela ukuthi sihlanganise i-database, ama-analytics kanye nokuqaliswa kwezinkinga ezingenhla zokusebenzisa kahle zibe yithuluzi elilodwa [7, 8, 9].
Kunama-algorithms amaningi (omabili esimanjemanje futhi akusiwona esimanje) okusesha imithetho yenhlangano kusethi yedatha. Ama-algorithms anjalo angahlukaniswa ngamaqembu amathathu:
- Ama-algorithms asebenzisa i-traversal of algebraic lattices (Lattice traversal algorithms)
- Ama-algorithms asuselwe ekusesheni amanani okuvunyelenwe ngawo (Umehluko- kanye nama-algorithms okuvumelana asethiwe)
- Ama-algorithms asuselwe ekuqhathaniseni ngakubili (Ama-algorithms okungeniswa kokuncika)
Incazelo emfushane yohlobo ngalunye lwe-algorithm yethulwa etafuleni elingezansi:
Ungafunda kabanzi mayelana nalesi sigaba [4]. Ngezansi kunezibonelo zama-algorithm ohlobo ngalunye:
Njengamanje, kuvela ama-algorithms amasha ahlanganisa izindlela ezimbalwa zokuthola ukuncika kokusebenza. Izibonelo zama-algorithms anjalo yi-Pyro [2] ne-HyFD [3]. Ukuhlaziywa komsebenzi wabo kulindeleke ezihlokweni ezilandelayo zalolu chungechunge. Kulesi sihloko sizohlola kuphela imiqondo eyisisekelo kanye ne-lemma edingekayo ukuze siqonde amasu okuthola ukuncika.
Ake siqale ngeyodwa elula - umehluko- kanye nesethi yokuvumelana, esetshenziswa ohlotsheni lwesibili lwama-algorithms. Umehluko-isethi isethi yama-tuples angenawo amanani afanayo, kuyilapho i-all-set, ngokuphambene, ama-tuples anamanani afanayo. Kuyaphawuleka ukuthi kulesi simo sicabangela kuphela ohlangothini lwesobunxele lokuncika.
Omunye umqondo obalulekile okuhlangatshezwane nawo ngenhla i-algebraic lattice. Njengoba ama-algorithms amaningi esimanje asebenza kulo mqondo, sidinga ukuba nombono wokuthi uyini.
Ukuze wethule umqondo we-lattice, kuyadingeka ukuchaza isethi e-oda ngokwengxenye (noma isethi e-oda ngokwengxenye, efushanisiwe njenge-poset).
Incazelo 2. Isethi S kuthiwa ihlelwa ngokwengxenye ngokuhlobene kanambambili ⩽ uma kukho konke a, b, c ∈ S izici ezilandelayo zaneliswa:
- Ukuvumelana nezimo, okungukuthi, a ⩽ a
- I-Antisymmetry, okungukuthi, uma u-⩽ b no-b ⩽ a, bese kuba ngu-a = b
- I-Transitivity, okungukuthi, ku-⩽ b no-b ⩽ c kulandela ukuthi a ⩽ c
Ubudlelwano obunjalo bubizwa ngokuthi i-(loose) partial order relation, futhi isethi ngokwayo ibizwa ngokuthi isethi e-oda ngokwengxenye. Isaziso esisemthethweni: ⟨S, ⩽⟩.
Njengesibonelo esilula sesethi e-odwe ngokwengxenye, singathatha isethi yazo zonke izinombolo ezingokwemvelo uN ngokuhlobana okujwayelekile kwe-oda ⩽. Kulula ukuqinisekisa ukuthi wonke ama-axiom adingekayo anelisekile.
Isibonelo esinengqondo kakhudlwana. Cabangela isethi yawo wonke amasethi angaphansi {1, 2, 3}, ahlelwe ngokuhlobana kokufakwayo ⊆. Impela, lokhu budlelwano kufeza zonke izimo zokuhleleka ngokwengxenye, ngakho-ke i-⟨P ({1, 2, 3}), ⊆⟩ iyisethi e-odwe ngokwengxenye. Isithombe esingezansi sibonisa isakhiwo sale sethi: uma isici esisodwa singafinyelelwa ngemicibisholo iye kwenye i-elementi, khona-ke basebudlelwaneni be-oda.
Sizodinga ezinye izincazelo ezimbili ezilula ezivela emkhakheni wezibalo - i-supremum ne-infimum.
Incazelo 3. Vumela ⟨S, ⩽⟩ kube isethi e-odwe ngokwengxenye, A ⊆ S. Umkhawulo ongaphezulu ka-A uyisici u ∈ S esifana nokuthi ∀x ∈ S: x ⩽ u. Ake u-U kube isethi yayo yonke imingcele engenhla ka-S. Uma kunento encane kakhulu ku-U, khona-ke ibizwa ngokuthi i-supremum futhi ichazwa ngokuthi u-sup A.
Umqondo wesilinganiso esiphansi ncamashi wethulwa ngokufanayo.
Incazelo 4. Vumela ⟨S, ⩽⟩ kube isethi e-odwe ngokwengxenye, A ⊆ S. I-infimum ka-A iyisici l ∈ S ngendlela yokuthi ∀x ∈ S: l ⩽ x. Vumela u-L kube isethi yayo yonke imingcele ephansi ka-S. Uma kunento enkulu ku-L, khona-ke ibizwa ngokuthi i-infimum futhi ichazwa ngokuthi inf A.
Cabanga njengesibonelo isethi ehlelwe ngenhla ⟨P ({1, 2, 3}), ⊆⟩ futhi uthole i-supremum ne-infimum kuyo:
Manje singakwazi ukwenza incazelo ye-algebraic lattice.
Incazelo 5. Vumela okuthi ⟨P,⩽⟩ kube isethi e-odwe ngokwengxenye ukuze yonke isethi engaphansi yezinto ezimbili ibe nesibopho esingaphezulu nesingaphansi. Khona-ke u-P ubizwa ngokuthi i-algebraic lattice. Kulesi simo, i- sup{x, y} ibhalwa ngokuthi x ∨ y, futhi inf {x, y} ngokuthi x ∧ y.
Ake sihlole ukuthi isibonelo sethu esisebenzayo ⟨P ({1, 2, 3}), ⊆⟩ i-lattice. Ngempela, kunoma yimuphi u-a, b ∈ P ({1, 2, 3}), a∨b = a∪b, kanye no-a∧b = a∩b. Isibonelo, cabangela amasethi {1, 2} kanye ne-{1, 3} futhi uthole i-infimum yawo kanye ne-supremum. Uma siziphambana nazo, sizothola isethi {1}, okuzoba i-infimum. Sithola i-supremum ngokuhlanganisa - {1, 2, 3}.
Kuma-algorithms okuhlonza izinkinga ezingokomzimba, isikhala sokusesha sivame ukumelwa ngendlela ye-lattice, lapho amasethi ento eyodwa (funda izinga lokuqala le-lattice yokusesha, lapho uhlangothi lwesobunxele lokuncika luqukethe isici esisodwa) simelela isibaluli ngasinye. yobudlelwano bokuqala.
Okokuqala, sibheka ukuncika kwefomu ∅ → Isibaluli esisodwa. Lesi sinyathelo sikuvumela ukuthi unqume ukuthi yiziphi izibaluli ezingokhiye abayinhloko (kulezi zibaluli azikho izinqumo, ngakho-ke uhlangothi lwesobunxele alunalutho). Ngaphezu kwalokho, ama-algorithms anjalo ahambela phezulu eduze kwe-lattice. Kuyaqapheleka ukuthi akusiyo yonke i-lattice engadalulwa, okungukuthi, uma ubukhulu obufunwayo bohlangothi lwesobunxele budluliselwa kokokufaka, khona-ke i-algorithm ngeke idlulele ngaphezu kwezinga elinalowo sayizi.
Isibalo esingezansi sibonisa ukuthi i-algebraic lattice ingasetshenziswa kanjani enkingeni yokuthola i-FZ. Lapha unqenqema ngalunye (X, XY) imele ukuncika X → Y. Isibonelo, siphumelele izinga lokuqala futhi siyazi ukuthi ukulutheka kuyagcinwa A → B (sizobonisa lokhu njengokuxhumana okuluhlaza phakathi kwama-vertices A и B). Lokhu kusho ukuthi ngokuqhubekayo, lapho sikhuphuka sigudla i-lattice, angeke sihlole ukuncika A, C → B, ngoba ngeke kusaba kuncane. Ngokufanayo, ngeke sikuhlole uma ukuncika bekubanjwe C → B.
Ngaphezu kwalokho, njengomthetho, wonke ama-algorithms esimanje osesha imithetho yenhlangano asebenzisa isakhiwo sedatha esifana nokuhlukanisa (emthonjeni wangempela - ukwahlukanisa okuhlutshiwe [1]). Incazelo esemthethweni yokuhlukanisa imi kanje:
Incazelo 6. Vumela u-X ⊆ R kube isethi yezibaluli zobudlelwano r. Iqoqo isethi yezinkomba zama-tuples ku-r anenani elifanayo lika-X, okungukuthi, c(t) = {i|ti[X] = t[X]}. I-partition iyiqoqo lamaqoqo, okungafaki amaqoqo obude beyunithi:
Ngamagama alula, ukwahlukanisa kwesibaluli X iyiqoqo lohlu, lapho uhlu ngalunye luqukethe izinombolo zomugqa ezinamavelu afanayo X. Ezincwadini zanamuhla, isakhiwo esimelela ama-partitions sibizwa nge-position list index (PLI). Amaqoqo obude beyunithi awabandakanyi izinjongo zokuminyanisa i-PLI ngoba angamaqoqo aqukethe kuphela inombolo yerekhodi enenani eliyingqayizivele okuzohlala kulula ukulibona.
Ake sibheke isibonelo. Ake sibuyele etafuleni elilodwa neziguli futhi sakhe ama-partitions amakholomu Isiguli и Ubulili (kuvele ikholomu entsha kwesokunxele, lapho izinombolo zomugqa wethebula zimakwe):
Ngaphezu kwalokho, ngokwencazelo, ukwahlukanisa kwekholomu Isiguli empeleni izobe ingenalutho, njengoba iqoqo elilodwa likhishiwe ekuhlukaniseni.
Ama-partitions angatholwa ngezici ezimbalwa. Futhi kunezindlela ezimbili zokwenza lokhu: ngokudlula etafuleni, yakha ukwahlukanisa usebenzisa zonke izimfanelo ezidingekayo ngesikhathi esisodwa, noma uyakhe usebenzisa ukusebenza kokuphambana kwezingxenye usebenzisa isethi yezimfanelo. Ama-algorithms okusesha umthetho we-Federal asebenzisa inketho yesibili.
Ngamagama alula, ukuze, isibonelo, uthole ukwahlukanisa ngamakholomu ABC, ungathatha ama-partitions AC и B (noma iyiphi enye isethi yamasethi angaphansi ahlukene) futhi uwaphambanise. Ukusebenza kokuphambana kwezihlukaniso ezimbili kukhethwa amaqoqo anobude obukhulu kakhulu avamile kuzo zombili izingxenye.
Ake sibheke isibonelo:
Esimweni sokuqala, sithole i-partition engenalutho. Uma ubhekisisa itafula, khona-ke ngempela, awekho amanani afanayo ezimfanelo ezimbili. Uma sishintsha kancane ithebula (ikesi elingakwesokudla), sizovele sithole impambana-mgwaqo engenalutho. Ngaphezu kwalokho, ulayini 1 no-2 empeleni uqukethe amanani afanayo ezibaluli Ubulili и Доктор.
Okulandelayo, sizodinga umqondo onjalo njengosayizi wokuhlukanisa. Ngokusemthethweni:
Kalula nje, usayizi wokuhlukanisa inani lamaqoqo afakwe ekuhlukaniseni (khumbula ukuthi amaqoqo angawodwa awafakiwe ekuhlukaniseni!):
Manje sesingakwazi ukuchaza eyodwa yama-lemmas angukhiye, okuthi ngokwehlukana okunikiwe sikwazi ukunquma ukuthi ukuncika kuphethwe noma cha:
Lema 1. Ukuncika A, B → C kubamba uma futhi kuphela uma
Ngokusho kwe-lemma, ukunquma ukuthi ukuncika kubambe, izinyathelo ezine kufanele zenziwe:
- Bala ukwahlukanisa ohlangothini lwesobunxele lokuncika
- Bala ukwahlukanisa ohlangothini lwesokudla lokuncika
- Bala umkhiqizo wesinyathelo sokuqala nesesibili
- Qhathanisa amasayizi ama-partitions atholakala esinyathelweni sokuqala nesesithathu
Ngezansi isibonelo sokuhlola ukuthi ukuncika kubambe ngokwale lemma:
Kulesi sihloko, sihlole imiqondo efana nokuncika kokusebenza, ukuncika okulinganiselwe kokusebenza, sabheka lapho esetshenziswa khona, kanye nokuthi yimaphi ama-algorithms okusesha imisebenzi engokwenyama akhona. Siphinde sahlola ngokuningiliziwe imiqondo eyisisekelo kodwa ebalulekile esetshenziswa ngokusebenzayo kuma-algorithms wesimanje ekusesheni imithetho yenhlangano.
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