Iigrafu kwinzululwazi yekhompyutha: inkcazelo, iintlobo, imizekelo isicelo. Igrafu theory kwinzululwazi yekhompyutha

Libalulekile indlela yekhompyutha ubudlelwane emisela kuhlanganiswa iziqalelo. Zizo ezo izinto ezisisiseko yokufunda theory kwigrafu.

iinkcazelo esisiseko

Yintoni kule grafu kwinzululwazi yekhompyutha? Oku kuquka ezininzi zezinto ekuthiwa iindawo okanye eziphezulu, ezinye izibini idityaniswe m. UN ezimbanjeni. Umzekelo, igrafu kulo mzobo (a) ibandakanya iindawo ezine, zibonakaliswe A, B, C, no-D, B oludityaniswe nganye ezinye eziphezulu iimbambo ezintathu, kwaye C no D nazo uxhulumanisa. iindawo ezimbini ezikufutshane ukuba idityaniswe emphethweni. Lo mzobo ubonisa indlela obabuthandwa yokwakha indlela iigrafu kwinzululwazi yekhompyutha. Iizangqa bamele eziphezulu kunye imigca kokuxhuma isibini ngasinye kuzo, ezi iimbambo.

Yintoni igrafu ezithuka ubizwa kwinzululwazi yekhompyutha? Yena ubudlelwane phakathi emancamini omabini iimbambo abantu macala. Ubambo ixhulumanisa nje kuzo kunye nabanye. Kwiimeko ezininzi, ke, kuyimfuneko ukuba ukuvakalisa ubudlelwane yezi ngu - umzekelo, ukuba A amanqaku B, kodwa awunakho ukwenza ngolunye uhlobo. Le njongo ke kwenkcazo igrafu kwi computer, sekunjalo iqulathe uluhlu lweendawo kunye iseti ezinemiphetho ngqo. edge nganye oriented kuthetha unxulumano phakathi eziphezulu ogama ulwalathiso sinentsingiselo. igrafu waqondisa zimveza, njengoko kubonisiwe kumfanekiso (b), ezinemiphetho zabo zimelwe iintolo. Xa ufuna ukugxininisa ukuba igrafu non-zemiyalelo, oko kuthiwa ndenzile.

models inethiwekhi

Iigrafu zesayensi lezekhompuyutha imodeli yemathematika izakhiwo womnatha. Lo mzobo ulandelayo ubonisa isakhiwo Internet, ngoko wamzalela igama ARPANET, ngoDisemba 1970, xa wayeneminyaka amanqaku-13 kuphela. Iindawo ngamaziko yokwenza kwaye iimbambo ukudibanisa eziphezulu ezimbini feedforward therebetween. Ukuba akuyihlawuli ingqalelo eUnited States inyanzele imaphu, yonke umfanekiso igrafu node-13 efana elidlulileyo. Kulo mzekelo, indawo kanye le incopho akuyomfuneko. Kubalulekile ukuba zeziphi iindawo ezidibene omnye komnye.

Ukusetyenziswa iigrafu kwi computer ivumela ukubona izinto mhlawumbi amaqhina oqhagamshelwano ngokwasemzimbeni okanye ngokusengqiqweni kwisakhiwo womnatha ngayo. node-13 ARPANET ngumzekelo kothungelwano lonxibelelwano apho iikhompyutha ngaphezulu okanye ezinye izixhobo basenokugqithisela imiyalezo, kunye ezinemiphetho bamele ikhonkco ngqo apho ulwazi enokusasazwa.

imizila

Nangona iigrafu zisetyenziswa kwiindawo ezininzi ezahlukeneyo, kuba iimpawu ezifanayo. theory Igrafu (inzululwazi computer) kubandakanya mhlawumbi yeyona ibalulekileyo kubo - ingcamango yokuba izinto rhoqo ukuhamba ecaleni emiphethweni, ngokulandelelana ukusuka node ukuya node, kuba oko umkhweli a moya ezimbalwa okanye ulwazi idluliselwe kumntu umntu womnatha ekuhlaleni, okanye umsebenzisi computer, gqolo ukutyelela inani lamaphepha web ngokulandela ilinki.

Le mbono ushukumisa kwinkcazelo indlela ngokweesirisi nodes eziqhagamshelene imiphetho. Maxa wambi kuyimfuneko ukuba siqwalasele indlela equlathe kuphela amacandelo, kodwa kwakhona ukulandelelana ezinemiphetho kokuxhuma kubo. Umzekelo, ukulandelelana eziphezulu MIT, BBN, NGOKWERANDI, UCLA na umzila ku kwigrafu ARPANET intanethi. Indlela nodes kunye nokuphela kwegqabi ukuze kuphindwa. Umzekelo, ESRI, uStan, UCLA, ESRI, Utah, MIT naye indlela. Indlela apho iimbambo aziphindwanga, ebizwa nomxokelelwane. Ukuba iindawo azinikezelwanga kuphindwa, ibizwa ngokuba nomxokelelwane elula.

imijikelo

eziphilayo ebalulekileyo iigrafu computer - it imijikelo nenika isakhiwo umsesane, ezifana kulandelelwano nodes LINC, ITYALA, CARN, HARV, BBN, MIT, LINC. Iindlela iimbambo ubuncinane ezithathu, apho esiludumbo yokuqala nezokugqibela ezifanayo, kwaye ke ezinye ezahlukeneyo, bamele iigrafu elibujikele kwi kwinzululwazi yekhompyutha.

Imizekelo: Umjikelo ESRI, uStan, UCLA, ESRI yeyona imfutshane, yaye ESRI, uStan, UCLA, NGOKWERANDI, BBN, Utah, ESRI kakhulu ngakumbi.

Phantse zonke ngohlangothi ARPANET le grafu bobabo kumjikelo. Oku kwenziwa ngabom, ukuba kukho kuwo uyasilela, ingabe ithuba utshintsho ukusuka node omnye komnye. Imijikelo konxibelelwano kunye neenkqubo zothutho babekho komsebenzi - zinika iindlela ezizezinye omnye umendo umjikelo. I-social networks zidla imijikelo buqapheleke. Xa ufumana, umzekelo, ukuba umhlobo isikolo esikufutshane ukuba umzala lomkakho okunene usebenza umzalwana wenu, oko kumjikelo entlantlu kuni, umfazi wakho, umzala wakhe, umhlobo wakhe esikolweni, umsebenzi wakhe (okt. E. wakho umzalwana), yaye ekugqibeleni kwakhona.

igrafu lixhulumene: definition (science computer)

Kungokwemvelo ukuba sizibuze ukuba kunokwenzeka ukususela node ngamnye ukuba naliphi na ilungu elisisiseko. Le grafu ibonisa ukuba kukho indlela phakathi zonke iperi eziphezulu. Umzekelo, uthungelwano ARPANET - enxulumene kwigrafu. Kunjalo enokuthethwa uninzi zonxibelelwano kunye ezothutho nothungelwano, njengoko injongo yazo kukuba ukwalathisa traffic ukusuka kwenye node ukuya kwenye.

Kwelinye icala, akukho sizathu priori ukulindela ukuba ezi ndidi iigrafu kwinzululwazi yekhompyutha bandile. Umzekelo, kwi-network zentlalo Akukho nzima ukuba nomfanekiso abantu ababini akadibananga omnye komnye.

izakhi

Ukuba Ikholamu wayamene computer, nazo kweyela iseti amaqhekeza aseleyo ezinxulumeneyo, amaqela nodes ukuba sisodwa kwaye musa gqiba nge. Umzekelo, Umfanekiso ubonisa iindawo ezintathu ezifana: eyokuqala - A no B, owesibini - C, D no-E, kwaye eyesithathu iqulathe i eziphezulu eseleyo.

Amacandelo igrafu amele elucwangciso olusezantsi lwe nodes, apho:

• kwama enekona ngalinye eya naluphi na olunye;
• yenye nje inxalenye iseti enkulu apho node ngamnye eya nayiphi na enye.

Xa iigrafu kwi computer yahlulwe kumacandelo abo, nto nje nenkcazelo sokuqala indlela yesakhiwo. Eli candelo inokuba zizityebi kubume lwangaphakathi, kubalulekile ukuba ukutyhilwa kwale network. Umzekelo, indlela esesikweni yovandlakanyo ngokubaluleka node kukuqinisekisa ukuba mangaphi amalungu iya kwahlulwa-hlulwa count, ukuba esiludumbo isusiwe.

ingxenye obukhulu

Kukho indlela ukulungiselela uvavanyo esemgangathweni inamacandelo connectivity. Umzekelo, kukho womnatha lonke yoluntu kunye unxibelelwano phakathi kwabantu ababini, ukuba ngabahlobo.

Uhlobene? Mhlawumbi akunjalo. Uqhagamsheleko - impahla kunokuba ethe, kwaye ukuziphatha node elinye (okanye iseti encinane kubo) unga nciphisa oko nto. Ngokomzekelo, umntu omnye kungekho abahlobo eziphilayo licandelo kuqulethe enekona enye, ngoko ke, le count iza alidityaniswanga. Okanye kwisiqithi esikude lemvula, ebandakanya abantu abangenalo ukunxibelelana nehlabathi ngaphandle, baya kuba yinxalenye encinane network, nto leyo engqina incoherence yayo.

inethiwekhi Global abahlobo

Kodwa kukho into enye. Umzekelo, umfundi wencwadi ethandwayo unabahlobo aziintanga kwamanye amazwe, aze abenze yingxenye eyodwa. Ukuba uthathe ingqalelo yokuba abazali zezi abahlobo kunye nabahlobo babo, bonke aba bantu nazo kwicandelo elifanayo, nangona engazange beva ngalo umfundi, abathetha ulwimi olwahlukileyo, yaye ecaleni akuzange. Ngoko ke, nangona uthungelwano lwehlabathi kuMhlobo - wayamene, umfundi uya zifakwe kwicandelo le-makhulu kakhulu, engena kuzo zonke iindawo zehlabathi, equka abantu abavela kwiindawo ezininzi ezahlukeneyo yaye, enyanisweni, iqulathe inxalenye enkulu yabantu ehlabathini.

Kwenzeka okufanayo kwi iiseti data kwinethiwekhi - ezinkulu iinethiwekhi, complex baqhele ukuba babe icandelo eliphezulu, esiquka elivisa zonke iindawo. Ngaphezu koko, xa lo womnatha ubandakanya icandelo eliphezulu, oko phantse lonk omnye kuphela. Ukuze siqonde isizathu sokuba, kuyimfuneko ukuba sibuyele umzekelo uthungelwano lwehlabathi nobuhlobo kwaye uzame ukucinga ubukho izakhi ezibini ezona zininzi, ngamnye elibandakanya izigidi zabantu. Kuyafuneka ukuba ubambo enye ezinye icandelo lokuqala ukuya yesibini amacandelo amabini ubuninzi zadityaniswa omnye. Ekubeni edge omnye kuphela, kwiimeko ezininzi ayinakwenzeka ukuba oko kwasekwa, kwaye kungoko amacandelo ubuninzi ezimbini networks ukho ze sebenzisa.

Kwiimeko ezithile ezinqabileyo, xa amacandelo amabini ubuninzi co-waphila ixesha elide kumsebenzi womnatha yokwenene, ubuhlobo babo ingalindelekanga, sedrama, kunye, ekugqibeleni, kuba nemiphumo enkulu.

Accident ingxenye naziphi

Ngokomzekelo, emva kokufika bamazwe baseYurophu kwi idla saseNtla Western malunga nesiqingatha iwaka leminyaka eyadlulayo, kwakukho na intlekele kwihlabathi. Ukusuka kwindawo ngembono inethweki, kukhangeleke ngokungathi oku: amawaka amahlanu iminyaka kwinethiwekhi yoluntu lwehlabathi, mhlawumbi yayibandakanya candelo ezimbini ezinkulu - nye kuMntla noMzantsi Merika, kunye nezinye - Asia. Ngenxa yesi sizathu, i-iteknoloji iye yaguquka ngokuzimeleyo kula macandelo mabini, kunye, ngakumbi, njengoko iqulunqwe nezifo zabantu, njalo njalo. D. Xa amacandelo amabini ekugqibeleni wakhwela technology kwebala kunye nesifo ngokukhawuleza elibi idla yesibini.

High School American

Ingcamango component obukhulu luncedo yokucinga malunga neenethiwekhi kwisikali ezincinane kakhulu. Umzekelo umdla igrafu obonisa ngonxulumano kwisikolo esiphakamileyo US kuba kwisithuba seenyanga ezili-18. Isibakala sokuba iqulethe icandelo iphezulu lubalulekile xa kufikwa ukusasazeka kwezifo, izifo ezidluliselwa ngeentlobano zesini, oko kukuthi, injongo yesi sifundo. Abafundi Kusenokwenzeka ukuba iqabane elinye kuphela ebudeni belo xesha, kodwa, nangona kunjalo, ngaphandle kokubonakala ngayo, ziye inxalenye amacandelo eliphezulu, yaye ngenxa yoko, inxalenye iindlela ezininzi ezinokuba yokosulela. Ezi zithinteli zibonisa ubuhlobo kusenokwenzeka ukuba kudala yaphela, kodwa ke ukudibanisa abantu ngemixokelelwane elide kakhulu, ukuba isihloko uhlolisiso olunzulu kunye ukuhleba. Noko ke, ukuba ngokwenene: izibakala zentlalo azibonakali, kodwa macrostructures osisiphumo abonakala yimveliso ulamlo ngamnye.

Kude kunye nobubanzi-yokuqala yokukhangela

Ukongeza inkcazelo malunga nokuba kwiindawo ezimbini oxhulumene indlela, ithiyori igrafu kwinzululwazi yekhompyutha ikuvumela ukuba ufunde ubude balo - kwezothutho, unxibelelwano okanye ukusasazwa iindaba kunye nezifo, kwakunye nokuba uhamba iincopho eziliqela okanye ezininzi.

Ukuze wenze oku, ukuchaza ubude indlela lilingana nenani amanyathelo iqulethe ukususela ekuqaleni ukuya ekupheleni, okt. E. Inani zinongqameko ngokulandelelana leyo. Umzekelo, MIT, BBN, NGOKWERANDI, indlela UCLA linobude-3, kwaye MIT, Utah - 1. Usebenzisa ubude umendo, sinokuthi xa kwiindawo ezimbini zicwangciswe kumhlathi ukusondelelana nabanye okanye kude ngamnye umgama phakathi iincopho ezimbini uchazwa ubude indlela mfutshane phakathi kwabo. Umzekelo, umgama phakathi LINC kunye ESRI yi-3, ke, ukuqinisekisa ukuba oku, kufuneka ukuba kuqinisekiswe ukuba akukho ubude esilingana 1 okanye 2, therebetween.

Nobubanzi-yokuqala algorithm search

Kuba umgama encinane igrafu phakathi ezimbini iindawo ubale ngokulula. Kodwa complex kukho imfuneko indlela eyondeleleneyo yokufumanisa imigama.

Eyona ndlela yendalo ukwenza oku yaye, ke ngoko, ngempumelelo kakhulu na (umzekelo, uthungelwano lwehlabathi abahlobo) zilandelayo:

• Bonke abahlobo kuthiwe zibekwe kumgama 1.
• Bonke abahlobo abahlobo (zamadoda sele ikhankanywe) ziya kwaziswa mgama 2.
• Bonke abahlobo babo (kwakhona, hayi ngokubala abantu enombhalo) umemezele kumgama kude 3.

Ukuqhubeka ngale ndlela, uphendlo oluqhutywa maleko ezilandelayo, ngasinye apho - on the unit kwi ezidlulileyo. umaleko nganye entsha ubunjwe nodes angakhange inxaxheba engaphambili, nokuba bawe ngohlangothi ukususela enekona esibekwa odlulileyo.

Le ndlela kuthiwa nobubanzi-yokuqala search, njengoko Uzifunela kumhlathi ngaphandle esiludumbo sokuqala, ikakhulu egubungele elilandelayo. Ukongeza ekunikezeleni indlela yokuqingqa imigama, oko unako ukukhonza njenge isakhelo sengqiqo luncedo ukuba aququzelele isakhiwo igrafu kwakunye yokwakha njani igrafu ye computer, ukuba iincopho ngokusekelwe kumgama kwabo isisiqalo elimisiweyo.

Ububanzi-yokuqala yokukhangela linokusetyenziswa nje kuphela womnatha abahlobo, kodwa nawuphi na igrafu.

umhlaba Small

Ukuba ubuyele womnatha kwihlabathi abahlobo, ungabona ukuba ukuxambulisana kuchaza ukuba ilungu icandelo eliphezulu ngokwenene emkholisayo into ngakumbi: hayi nje kuphela ukuba umfundi asele iindlela kubahlobo, odibanisa naye elivisa yabantu ehlabathini, kodwa ke ezi iindlela eminye yayo elifutshane .

Le mbono ubizwa ngokuba "ngumkhuba yehlabathi elincinane": ihlabathi kubonakala encinane, ukuba ucinga ngento indlela emfutshane inxibelelanisa naziphi na abantu ababini.

Ingcamango "nokuxhawulana emithandathu" kuqala ngokomfuniselo uphando yi Stanley Milgram kunye noogxa bakhe 1960. Ngaphandle kokuba naluphi na uluhlu lwe data yenethiwekhi yoluntu, kunye nohlahlo lwabiwo-$ 680, wagqiba ukujonga ngaphandle ingcamango ethandwayo. Ukuza kuthi ga ngoku, wabuza 296 lwabasunguli randomly ekhethiweyo uzama ukuthumela ileta eya wezabelo, owayehlala kwidolophu eBoston. Lwabasunguli banikwa ulwazi lobuqu malunga nenjongo (kuquka idilesi kunye wobungcali), kwaye kwafuneka ukuba ukuthumela ileta eya kulo mntu abangabaziyo ngegama, kunye nemiyalelo efanayo, ukuze ifike njongo ngokukhawuleza kangangoko kunokwenzeka. unobumba ngamnye ocande ezandleni eziliqela abahlobo, ebumba umxokelelwane luvalwa imfuyo brokers ngaphandle kwe eBoston.

Phakathi imixokelelwane 64 eziye kufikelela ithagethi, ubude engumndilili ezintandathu, engqina inani ogama engamashumi amabini ngaphambili kulo mdlalo isihloko Dzhona kaGera.

Nangona zonke iintsilelo kwesi sifundo, ukucikideka wabonisa enye yeendlela ezibalulekileyo ukuqonda kwethu kuxhumana. Kwiminyaka eyalandelayo kulo wenziwa sigqibo ngokubanzi: social networks akholisa ukuba iindlela ezimfutshane kakhulu phakathi ngababini esicalanye zabantu. Kwaye nokuba Kuqhagamshelwano olunjalo ngqo kunye neenkokheli zoshishino kunye neenkokeli zezopolitiko musa ukuhlawula ngokwabo yonke imihla, ubukho iindlela ezimfutshane hlobo idlala indima enkulu kakhulu kwisantya yokusasaza ulwazi, izifo kunye nezinye iintlobo zosuleleko ekuhlaleni, kwakunye nokufikelela ngamathuba social networking inika abantu kakhulu iimpawu esahlukileyo.