
avakashangal (nyayamaaya vibhajanam)

nyayamaaya vibhajanathile avakasham oru kalikkaaran labhikkumenn pratheekshikkavunna vibhavangaludeyo charakkukaludeyo anupatham vivarikkunnu. pala nyayamaaya vibhajana krameekaranagalilum, ellah ejantumaarkkum "thulya avakashangal" undu, athaayath oro ejantumaarkkum vibhavathinte 1/"enn" labhikkaan arhathayund. ennaal ejantumaarkku "vyathyastha avakashangal" ulla praayogika krameekaranangalund. chila udaaharanangal
avakaashathekkurichulla saadhaarana ashayathe adisthaanamaakkiyullathaanu eee ashayam. oru sahakarana geyimil sammathikkukayum athinte moolyam avakaashamaayi upayogikkukayum cheythukondu avakashangal nirnnayikkaan kazhiyum.
ejantumaarkku thulya avakashangal ullappol, pariharam anjjaathathvathinte soothravaakyathe thripthippeduthanamennu aavashyappedunnathu nyaayayukthamaan (samamiti ennum vilikkunnu), athaayath ejantumaare avarude moolyanirnnayangalaal maathrame pariganikkoo, avarude perukalalla. ithinu vipareethamaayi, ejantumaarkku vyathyastha avakashangal ullappol, anjjaathathvam sadhuvalla, pariharangal asamamayirikkanam.
vyathyastha avakashangalulla nyayamaaya vibhajanathinte vividha prasnangal padikkappettittund.
panam vibhajikkuka.
panam maathram vibhajikkukayum oro sweekarthaavinum chila nischitha thuka vyakthamaakkukayum cheythittundenkilum, prashnam sankeernamaayirikkum. nirddishta thukakal panatthinte thukayekkaal kooduthalo kuravo aakam, laabhamo nashtamo pinneedu pankidendathundu. aanupathika niyamam innu niyamathil saadhaaranayaayi upayogikkunnu, ithu paapparattha sidhaanthathile sthiramaaya anumaanamaan. ennirunnaalum mattu niyamangal palappozhum upayogikkunnu, udaaharanathina
thalmoodil.
aanupaathikamaayi avakashangal theerumaanikkappedaatha niravadhi udaaharanagal thaalmoodil undu.
eee parihaarangalellam sahakarana geyimukal vazhi maathrkayaakkaam. estettu division prashnathinu oru valia saahityamundu, geyim sidhaanthathil roobert jeey aanu ithinu aadyamaayi oru saidhaanthika adisthaanam nalkiyathu. 1985-leeii oomanum maikkal masler. malsaricha vasthra niyamam kaanuka.
thudarchayaaya vibhavangal vibhajikkuka.
oru vaividhyamaarnna thudar vibhavathe vibhajikkunna prasnamaanu nyayamaaya kekku murikkal. vyathyastha avakaashangale maanikkunna aanupaathikamaaya kekku murikkal ellaayppozhum nilavilundu. rund pradhana gaveshana chodyangal (eiii) oru nyayamaaya vibhajanathinu ethra vettikkuravukal aavasyamaanu? (bii) oru division kanakkukoottaan ethra chodyangal aavasyamaanu? nokkuka
claude computing parithasthithikalkku onniladhikam ekeekritha vibhaajya vibhavangale vibhajikkendathundu (udha.jii. oro upayokthaavinum vyathyasthamaaya vibhavangalude samyojanam aavasyamulla upayokthaakkalkkidayil memory allengil cpu). ejantumaarkku vyathyastha avakashangal undakavunna krameekaranam aandu.
nyayamaaya inam vihitam.
samana avibhaajya enangal-paarlamentukalile seettukal vibhajikkuka.
aanupathika praathinidyamulla paarlamentari janaadhipathya rajyangalil oro partic athinte vottukalude ennathinu aanupaathikamaayi seettukalkku arhathayund. bahu-bharanaghadanaa samvidaanangalil, oro niyojakamandalathinum athinte janasamkhyayude anupaathathil seettukalkku arhathayund. samana avibhaajya enangale (seettukal) vyathyastha avakashangalulla ejantumaarkkidayil vibhajikkunna prashnamaanith. ithine vibhajana prashnam ennu vilikkunnu.
janasamkhyayude valippam anusarichu seettukal anuvadikkunnathu cheria niyojakamandalangale shabdamillaathe avasheshippikkum. thulya valippamulla niyojakamandalangal undaayirikkuka ennathaanu ettavum eluppamulla pariharam. ennirunnaalum, chilappol ithu asaadhyamaanennu theliyikkaam-udaaharanathinu, europian unionilo americayilo. votting power' niyojakamandalangalude valippathin aanupaathikamaanennu urappaakkunnath avakaashathinte prasnamaanu.
vyathyastha valippathilullatho bharamullatho aaya niyojakamandalangalkk votting shakti kanakkaakkunna niravadhi reethikalundu. shappy-shubik power indux, banshaff power indux ennivayaanu pradhaanamaayath. eee power induxukal niyojakamandalangalkk penros reethi nalkunnathupole eathu kramarahithamaya reethiyilum waitinginte varggamoolavumaayi ekadeshamaayi cheraamennu anumaanikkunnu. eee anumaanam yadhaartha sambradaayavumaayi poruthappedunnilla, valia niyojakamandalangalodu avar anyaayamaayi perumaarunnu ennathu vaadayogyamaanu.
vaividhyamaarnna avibhaajya enangal.
nyayamaaya inam vihithathinte kooduthal sankeernamaaya krameekaranatthil, vyathyastha aalukalkk vyathyastha moolyangalulla onniladhikam vyathyastha enangalundu.
ejantumaar avarude samboornna yoottility pravarthanangalkku pakaram enangalil oru saadhaarana ranking maathram velippeduthumbol, vyathyastha avakashangalulla ejantumaarkku aanupaathikathayum asooya-swaathanthryavum assis, gaspezhs, mccansey, walsh enniva nirvachikkunnu. orupakshe aanupaathikamaaya" (ejantu rankingumaayi poruthappedunna oru yoottility profilinengilum aanupaathikamaayi) allengil "anivaryamaayum aanupaathikamaayi" (rankingumaayi poruthappedunna ellah yoottility profileukalkkum aanupaathikamaayi) oru alokkeshan undo ennu parishodhikkunnathinaayi avar oru polynomial-time algoritam avatharippikkunnu.
farhadi, ghodsi, hajiyaaghaayi, laahi, pennock, seddigin, seddigin, yaami enniva vyathyastha avakashangalulla ejantumaarkku maximine shareinte saamaanyavalkkaranamaayi waited maximine shareine (wms) nirvachichu. dablyuemmukalkk ettavum mikacha gunana gyaarandi pothuve 1/"enn" aanennum oro ejantinu oro gunanathinteyum moolyam paramavadhi ejantinte doubleum aayirikkunna prathyeka saahacharyathil randilonnu aanennum avar kaanichu. assis, chaan, lii ennivar wms enna ashayam jolikalilekku (negatteevu yoottilittikalulla enangal) maatti. rund ejantumaarkku polum dablyuemminte naalil kooduthal urappu nalkunnathu asaadhyamaanennu avar kaanichu (jolikal cheyyumbol, ekadesha anupatham onninekkaal valuthum cheruthum mikachathaanennu shradhikkuka). avar rund ejantumaarkkaayi 3/2-wms ekadesha algorithavum bainari moolyanirnnayangalulla enn ejantumaarkkaayi oru wms algorithavum avatharippikkunnu. avar moongakale nirvachikkunnu, ithu thannirikkunna saahacharyathil kaivarikkaan kazhiyunna dablyuemmukalude opttimal ekadeshamaanu. avar oru polynomial-time algoritam avatharippikkunnu, athu moongakalude 4-factor ekadesha kanakk nedunnu.
oru ejantinte cardinal yoottilittikal maarukayaanengil, ejantinte dablyuemmukale thripthippeduthunna bandilukalude koottam mariyekkaam ennathil wms oru "cardinal" aashayamaanu. babayof, nizan, talgam-kohen ennivar vyathyastha avakashangalulla ejantumaarkku mmsinte mattoru parivartthanam avatharippichu, ithu ejantinte bandilukalude "oordinal" rankingine maathram adisthaanamaakkiyullathaanu. bajattukal avakaashangalkk aanupaathikamaaya vyathyastha bajattukalumayulla malsara santhulithaavasthayiloodeyaanu eee nyaayabodham kaivarikkunnathenn avaa kaanikkunnu. chakrabarty, segal-halevi, suxompong ennivar eee nyaayabodhathe oordinal maximine share (ooms) ennu vilikkunnu. vividha oordinal mms ekadesha kanakkukal thammilulla bandham segal-halevi kooduthal padikkunnu.
babayof, isra, feej enniva oomsinekkaal sakthamaaya mattoru saadhaarana ashayam avatharippikkunnu, athine avar "eathenkilum vila vihitam (apps)" ennu vilikkunnu. avar oru polynomial-time algoritam kaanikkunnu, athu aapsinte 3/5-fraction nedunnu.
assis, moulin, sandomirsky enniva sakthamaaya oru polynomial time algoritam avatharippikkunnu, athu ellaayppozhum vyathyastha avakashangalum ekapaksheeyamaaya (positteev allengil negatteevu) moolyanirnayangalumulla ejantumaarkkaayi oru paretto-opttimal, dablyu. prop (0,1) alokkeshan kandethunnu.
vephinte elavukal ithuvare charakkukalk maathramaayi padikkappettittund. chakrabarty, igarashi, sucsumpong ennivar wef (1,0)-naayi waited raundu robin algoritam avatharippichu. thudarnnulla oru kruthiyil, chakrabarty, shmidt-crapellin, sucsumpong ennivar waited raundu-robin algoritam general picking-seekwansukalaayi saamanyavalkkarikkukayum eee seekwansukalude vividha monotonity propertykal padikkukayum cheythu.
saadhanangalum panavum.
vasthukkaludeyum panatthinteyum nyayamaaya vihitam enna prashnatthil, avibhajyamaaya charakkukalude krithyamaaya neethi nedaan saambathika kaimaattam upayogikkaam.
oro ejantinteyum (enangalude moolyavum "i" nuu nalkia panavum ennu nirvachichirikkunna) upayogakshamatha "r" ti ui "(ellah ejantumaarkkum" r "orupoleyaanengil) oru alokkeshane" thulya "ennu corady corady nirvachikkunnu.
avar "r"> = 1 ennathukondu thulyamaaya vihitam kandethunna oru algoritam avatharippikkunnu, athaayath vihitavum aanupaathikamaanu.
vilapeshal.
praayogikamaaya yoottility vektarukalude oru koottatthinte pravartthanamenna nilayil yoottilittikalude praayogika vector thiranjedukkunnathinulla amoortha prasnamaanu sahakarana vilapeshal (nyayamaaya vibhajanam vilapeshalinte oru prathyeka kesaanu).
moonnu classic vilapeshal parihaarangalkk vyathyastha avakashangalulla ejantumaarkku vyathyastha vakabhedangalundu. prathyekichum

