Graphs mu kombiyuta zvesayenzi: tsanangudzo, mifananidzo, kushanda mienzaniso. Graph dzidziso iri kombiyuta zvesayenzi

Hazvibatsiri mu nzira kombiyuta Pakusarudza ukama ikashandiswa zvinhu. Ndivo zvinokosha zvinhu kudzidza girafu dzidziso.

zvinhu tsanangudzo

Zviri girafu iri kombiyuta zvesayenzi? Anosanganisira muzvizhinji zvinhu anonzi nodes kana vertices, zvimwe yegwara ayo zvakabatana ne m. N. mbabvu. Somuenzaniso, girafu ari mufananidzo (a) ine nodes mana, runotaurwa A, B, C, uye D, B iyo zvakabatana nerimwe vertices mbabvu nhatu, uye C uye D vari zvakabatana. nodes maviri vari pedyo kana vari zvakabatana nemunhu mucheto. The mufananidzo inoratidza hwezuva nzira kuvaka sei calculators computer nesayenzi. Madenderedzwa vanomirira vertices uye mitsetse unobatanidza vaviri nomumwe wavo, ndizvo mbabvu.

Chii undirected girafu akadanwa kombiyuta zvesayenzi? Iye hukama pakati miviri yechifunhiro mbabvu vari zvakafanana, ichibata. Rumbabvu kungoti richibatanidza navo mumwe. Zvisinei, kazhinji kacho, zvinokosha kutaura asymmetric ukama - somuenzaniso, kuti A anotaura B asi kwete vakutarisire. chinangwa ichi ndiyo tsanangudzo girafu iri kombiyuta, richine chine nodes ane iine rinotungamirirwa kumicheto. Mumwe akatarisa kumucheto ndiko kubatana pakati vertices ane mirayiridzo hune. Akatungamirira calculators unoratidza, sezvinoratidzwa Figure (b), avo micheto vanomirirwa miseve. Kana uchida kusimbisa kuti vasiri achitaura girafu, kunonzi undirected.

samambure mienzaniso

Graphs mu kombiyuta nesayenzi vari kwemasvomhu muenzaniso samambure zvivako. Zvinotevera nhamba inoratidza nemamiriro Indaneti, akamuberekera zita ARPANET, muna December 1970, apo akanga 13 chete pfungwa. The nodes vari processing nzvimbo uye mbabvu kubatanidza vaviri vertices feedforward therebetween. Kana musingadi kuteerera United States waiita mepu, vamwe mufananidzo uri 13-raiva pedyo nebundu girafu chakafanana yapfuura mumwe. Panyaya iyi, chaiwo nzvimbo vertex hakusi kunokosha. Zvakakosha izvo nodes vari chokuita nomumwe.

Kushanda calculators iri kombiyuta anobvumira kuona sei zvinhu kana mumuviri kana zvine musoro interconnected mumidziyo mamiriro. 13-raiva pedyo nebundu ARPANET muenzaniso yokukurukurirana samambure umo pamusoro makombiyuta kana zvimwe mano anogona kutapurira mashoko, uye micheto zvinomiririra kwainge iro mashoko inogona kutapukira.

pakutengeserana

Kunyange zvazvo calculators anoshandiswa munzvimbo dzakawanda dzakasiyana, vane zvakafanana zvinhu. zvichida Graph dzidziso (kombiyuta science) kunosanganisira kukosha vavo - pfungwa yokuti zvinhu kazhinji zvinokambaira micheto, sequentially kutamira kubva raiva pedyo nebundu kuti raiva pedyo nebundu, kuva nazvo mufambi ane ndege shoma kana ruzivo chakasvitswa pamunhu nomunhu ari social network, kana mushandisi kombiyuta, nguva ndichishanyira nhamba yemapeji nokutevera Links.

Pfungwa iyi chinokurudzira tsanangudzo nzira sezvo nhevedzano nodes chokuita ne kumicheto. Dzimwe zvakafanira kufunga nzira kuti rine kwete chete zvinoriumba, asi vo kutevedzana kwezviitiko micheto unobatanidza pavo. Somuenzaniso, ari kutevedzana kwezviitiko vertices with, BBN, Rand, UCLA ari nzira iri ARPANET Internet girafu. Kufamba nodes uye micheto zvingadzokororwa. Somuenzaniso, SRI, STAN, UCLA, SRI, Utah, with ariwo nzira. Nzira iyo mbabvu zvisina kudzokororwa, inonzi cheni. Kana nodes zvisina kudzokororwa, inonzi iri nyore cheni.

zvinogara

mhando kukosha mune kombiyuta calculators - nayo zvinogara inomiririra rin'i chimiro, akadai kutevedzana kwezviitiko nodes LINC, CASE, CARN, HARV, BBN, with, LINC. Routes vane mbabvu zvitatu, umo okutanga nookupedzisira raiva pedyo nebundu ndiwo chete, uye vamwe vari zvakasiyana, vanomiririra cyclic calculators computer nesayenzi.

Mienzaniso: SRI kutenderera, STAN, UCLA, SRI ndiyo, uye SRI, STAN, UCLA, Rand, BBN, Utah, SRI zvakati zvikuru.

Zvinenge zvose ARPANET pamucheto girafu ndohwavo ichitanga. Izvi zvaitwa nemaune, kana ani wavo zvinopera, zvichaitawo mukana achichinja kubva rimwe raiva pedyo nebundu kune mumwe. Zvinogara zviri zvokufambisa uye yokufambisa nehurongwa varipo kuti redundancy - wavanotipa dzimwe nzira imwe kutenderera nzira. Kazhinji The Social network vari oneka zvinogara. Kana wawana, Somuenzaniso, kuti shamwari chikoro yepedyo hama mudzimai wako chaizvoizvo anoshanda mukoma wako, ndiwo kutenderera kuti chinosanganisira iwe, mudzimai wako, wake hama, shamwari yake kubva kuchikoro, mushandi wake (kureva. E. Your munin'ina), uye pakupedzisira iwe zvakare.

Kunofambidzana girafu: tsananguro (kombiyuta science)

Ndezvomuzvarirwo kuti hameno kana zvichibvira kubva mumwe raiva pedyo nebundu kusvika chero raiva pedyo nebundu. The girafu zvakabatana kana paine pakati peya dzose vertices nzira. Somuenzaniso, mashoko ARPANET rezvebonde - kwakabatana girafu. The chete zvinogona kutaurwa pamusoro vazhinji pakukurukurirana uye yokufambisa network, sezvo avo chinangwa kutungamirira motokari kubva raiva pedyo nebundu kune mumwe.

Ukuwo, hapana chikonzero priori kutarisira kuti mhando iyi calculators mu kombiyuta nesayenzi zvakapararira. Somuenzaniso, muna pasocial network hakusi nyore kufungidzira vanhu vaviri vasina ukama nepedyo.

zvinoriumba

Kana mbiru haisi kubata kuti kombiyuta, ivo muropa anowira kutaridza chokuita zvimedu, mapoka nodes kuti voga uye regai piringisha. Somuenzaniso, Figure unoratidza zvitatu zveefa dzakadaro: wokutanga - A uye B, wechipiri - C, D uye E, uye wechitatu unosanganisira vertices yasara.

Zvinoumba ari girafu vanomiririra subset pakati nodes, umo:

• mumwe vertex subgroup ane nzira kune umwe;
• subset haisi chikamu chikuru yakatarwa umo mumwe raiva pedyo nebundu ane nzira kune umwe.

Kana calculators iri kombiyuta vari rakakamurwa zvinoriumba dzavo, ndiko chete tsananguro nzira mamiriro avo kutanga. chikamu ichi kungava vakapfuma dzomunyika chimiro, zvakakosha kuti kududzirwa samambure. Somuenzaniso, wevakadzidza nzira dzokuziva rimwe raiva pedyo nebundu kukosha ndechokuti kuziva kuti zvikamu zvizhinji vachapesana count, kana raiva pedyo nebundu chinobviswa.

Maximum zvinoriumba

Pane nzira Qualitative tinyatsonzwisisa connectivity zvinoriumba. Somuenzaniso, pane yose pasocial network ine kubatana pakati vanhu vaviri, kana vari shamwari.

Zvakabatana? Zvichida kwete. Connectivity - asi kusimba pfuma, uye maitiro rimwe raiva pedyo nebundu (kana chiduku vanochengeta wavo) anogona kuderedza kuti chinhu. Somuenzaniso, mumwe munhu asina shamwari zvipenyu chinhu chinoumba ina chete vertex, uye naizvozvo, count haringapiwi kwakabatana. Kana munhu chitsuwa kure dzinopisa, iine vanhu vasina kuonana kunze nyika, achava diki chezvinonhuwira pomumbure, izvo zvinosimbisa incoherence kwayo.

Global Network shamwari

Asi pane chimwe chinhu. Somuenzaniso, mumwe muverengi chakakurumbira bhuku rine shamwari vakakurira dzimwe nyika, uye anoita kuti mumwe chikamu. Kana isu kufungawo vabereki shamwari idzi uye neshamwari dzavo, zvose izvi vanhu vari mune imwe zvinoriumba, kunyange vakanga vasati vanzwa pamusoro muverengi, vanotaura mumwe mutauro, uye pedyo hazvina kumbobvira. Saka, kunyange zvazvo yose samambure ushamwari - kwete chokuita, muverengi vachamutswawo mu rokuti yakakura chaizvo, rakapinza kumativi ose enyika, izvo zvinosanganisira vanhu vanobva kwakasiyana-siyana uye, chaizvoizvo, rine chikamu chinokosha vemo nyika.

The chete rinowanikwa muna zvakarukwa Data rinovira - guru, network kunzwisisa kazhinji vaifanira pakuderedza, rinosanganisira chinokosha inorwara nodes zvose. Uyezve, kana nemambure unosanganisira kunonyanyisa pakuderedza, zviri inenge nguva imwe chete. Kuti tinzwisise nei, zvinokosha kudzokera muenzaniso yose samambure ushamwari uye edza kufungidzira kuvapo vaviri kunonyanyisa zvinoriumba, chimwe nechimwe kunosanganisira mamiriyoni evanhu. Anofanira kuva chimwe rumbabvu pane vamwe rokutanga pakuderedza kune wechipiri kunonyanyisa maviri zvinoriumba akabatanidza kupinda chimwe. Sezvo kumucheto imwe chete, kazhinji zviri hakungagoni harina kuumbwa, uye nokudaro kunonyanyisa zvinoriumba mbiri chaidzo network vari kumbobvira kuchengetwa.

Mune zvimwe zvisingawanzoitiki zviitiko, kana zvakamisa hurongwa maviri kunonyanyisa co-aripo kwenguva refu ari chaiyo network, mubatanidzwa wavo akanga chisingatarisirwi, zvinoshamisa, uye, pakupedzisira, vane nemafashamo yakaipa.

Accident zvinoriumba batanidzo

Somuenzaniso, pashure kuuya vatsvakurudzi European muna nebudiriro iri Western Hemisphere pamusoro hafu nemireniyumu apfuura, paiva yose dambudziko. Kubva pfungwa nemaonero pomumbure, zvaiita sezvizvi: makore zviuru zvishanu yose pasocial network, zvichida raiva vaviri hofori zvinoriumba - mumwe North neSouth America, uye mumwe - muna Eurasia. Nokuda kwechikonzero ichi, unyanzvi rave vakashanduka pasina muna maviri zvinoriumba, uye, kunyange kuipa, sezvo akakudziridza uye chirwere kwevanhu, uye zvichingodaro. D. Kana hurongwa maviri pakupedzisira nekuonana zvemichina uye chirwere nokukurumidza uye disastrously dzakayerera wechipiri.

American High School

Pfungwa kufadza zvinoriumba runobatsira pfungwa pamusoro network pamwero muduku zvikuru. Muenzaniso kunakidza chinhu girafu pokuenzanisira ukama ari US chesekondari mumwedzi 18-nguva. Chokwadi kuti rine kunonyanyisa zvinoriumba kunokosha kana totaura kupararira kwezvirwere, zvirwere zvinotapuriranwa pabonde, inova chinangwa pakudzidza. Students vangadaro vaiva chete nemumwe chete panguva iyoyo, asi, zvakadaro, pasina ndazviziva, kunge chikamu zvinoumba kufadza, uye naizvozvo, chikamu dzakawanda zvinogona migwagwa ine hutachiwana. zvivako izvi zvinoratidza ukama kuti angave refu kupera, asi ivo batanidza vanhu yakarebesa namaketani, kuti nyaya kuongororwa zvakasimba uye makuhwa. Kunyange zvakadaro, havana zvechokwadi: sei pasocial chokwadi hazvioneki, asi dzinokosha macrostructures yakabuda sezvo chibereko nomumwe Mediation.

Distance uye upamhi-kutanga kutsvaka

Kuwedzera ruzivo pamusoro kana nodes vaviri zvakabatanidzwa nzira, girafu dzidziso iri kombiyuta sayenzi unokubvumira kudzidza pamusoro kureba - mu zvekufambisa, kukurukurirana kana kufambiswa nhau uye zvirwere, uyewo kana ichipfuurapo akawanda nenhongonya kana vakawanda.

Kuti aite izvi, ndeakaita nzira pakureba akaenzana kuwanda kwenhambwe kuti rine kubvira pakutanga kusvikira pakupedzisira, kureva. E. Nhamba micheto mu kutevedzana kuti. Somuenzaniso, with, BBN, Rand, UCLA nzira ine kureba 3, uye with, Utah - 1. Kushandisa kureba nzira, tinogona kutaura kuti kana nodes vaviri vari yakarongwa mbiru pedyo nomumwe kana kure kure pakati nenhongonya maviri kunotsanangurwa nokureba pfupi pakati pavo nzira. Somuenzaniso, daro pakati LINC uye SRI ndiye 3 Zvisinei, kuti tive nechokwadi ichi, zvinokosha kuti ritsigire kusavapo urefu zvakaenzana 1 kana 2, therebetween.

Noupamhi-kutanga kutsvaka algorithm

Nokuti muduku girafu kure pakati maviri nodes overenga nyore. Asi nokuti kunzwisisa pane kudikanwa hurongwa nzira dzokuziva marefu.

Zvikuru zvakasikwa nzira yokuita izvi, uye naizvozvo, inonyatsobudirira ndiyo inotevera (somuenzaniso, munyika yose richikurukura shamwari):

• Shamwari All vanonzi riri chinhambwe 1.
• Shamwari All shamwari (pasingaverengwi kare ataurwa) vari chiziviso kure 2.
• Shamwari dzavo dzose (zvakare, pasingaverengwi akanzi vanhu) vakazivisa pamusoro kure kure 3.

Achienderera mberi saizvozvi, kutsvaka rinoitwa mu nekutambira akaturikidzana, rimwe nerimwe - pamusoro chairema pamusoro yaimbovapo. Kuurungana itsva rinoumbwa nodes asina chikamu yapfuura ndivo, uye kuti vawe unopinza kubva vertex pakati yapfuura rukoko.

nzira iyi inonzi noupamhi-kutanga kutsvaka, sezvo iye anotsvaka mbiru kubva kwokutanga raiva pedyo nebundu, zvikurukuru akafukidza inotevera. Kuwedzera pakupa nzira nokuda Pakusarudza marefu, unogona kushanda yaibatsira Conceptual framework kuronga girafu mamiriro uyewo sei kuvaka girafu kombiyuta, ndine nenhongonya kwakavakirwa kure yakatarwa pokutangira.

Upamhi-kutanga kutsvaka ingashandiswa kwete chete kuti samambure shamwari, asiwo kune girafu.

Small nyika

Kana iwe dzokera munyika richikurukura shamwari, unogona kuona kuti kupopotedzana kuti inotsanangura kuva kufadza zvinoriumba zvechokwadi yaanofarira chinhu zvakawanda: kwete chete muverengi ane zvinoita kuti shamwari, unobatanidza naye inokosha zvinoenderana chavagari nyika, asi nzira izvi zvinoshamisa pfupi .

Pfungwa iyi kunonzi "duku chakajairika nyika": nyika inoratidzika diki, kana uchifunga chii pfupi nzira rinobatanidza chero mbiri vanhu.

Dzidziso "handshakes nhanhatu" yakatanga experimentally kuongororwa ne Stanley Milgram nevamwe vake vari Kuma1960. Asina chero akaisawo pasocial network data, uye ane mari kuti $ 680, akasarudza tarisa yakakurumbira pfungwa. Kuti izvi zvidaro, akabvunza 296 initiators randomly vakasarudzwa edza kutumira tsamba kuna stockbroker, vaigara weChicago Boston. Initiators vakapiwa mamwe mashoko nezvechinangwa (kusanganisira kero uye basa) pachavo, uye vaifanira kutumira tsamba kune munhu vavakanga nezita, nemirayiridzo chete, saka kuti yakasvika chinangwa nokukurumidza sezvinobvira. tsamba neimwe wakapfuurira ramaoko nhamba shamwari uye akaumba ngetani anovhara kuti hunde nevaichinja kunze Boston.

Pakati ngetani 64 kuti kwasvika chipfuro, paavhareji kureba kwakanga nhanhatu, achisimbisa nhamba ainzi makumi maviri apfuura vari kutamba Dzhona Gera rokuremekedza.

Pasinei zvose zvinokanganiswa kudzidza ichi, kuedza kwakaratidza chimwe chezvinhu zvinokosha zvinoumba manzwisisiro atinoita network. Mumakore akatevera kubvira rakaitwa yakakura mhedziso: network vanowanzotevedzera kuva nzira pfupi zvikuru pakati zvemasanga yegwara vanhu. Uye kunyange kana izvozvo zvisina kunanga kubatana nevatungamiriri vemabhizimisi uye vatungamiriri vezvematongerwo enyika havana kubhadhara pachavo zuva nezuva, kuvapo vakadaro pfupi migwagwa papfungwa basa pakukurumidza mashoko kufambiswa, chirwere uye dzimwe mhando chirwere munharaunda, uyewo kuwana mikana pasocial network anopa vanhu vane zvakasiyana unhu.