
kaee-prayaas mahanagar

multiple-trie metropolis (aim. tii. aim.) ack namuna lene kii vidhi haye joe mahanagar-husting vidhi kaa ack sanshodhit roop haye, jise pahali baar 2000 mein liu, liang aur wong dwara prastut kiya gayaa thaa.
ise namuna prakshepavakra koo teji seey parivartit karane mein madad karane key liye design kiya gayaa haye,
kadam key aakar aur sweekriti darr donon koo badhaakar. 
prishthabhoomi.
mahanagar-shikaar key saath samasyaaen.
markov chain monte carlo mein, mahanagar-husting algorithm (aim. aich.) kaa upayog sambhaavyata vitaran seey namuna lene key liye kiya jaa sakata haye, jiska seedhe namuna lena mushkil haye. haalaanki, aim. aich. algorithm key liye upayogkarta koo ack prastaav vitaran kii aapoorti karane kii aavashyakta hoti haye, joe apekshaakrit manmana hoe sakata haye. kaee mamalon mein, koee bhee formula _ 1 key sambhaavyata sthaan mein vartamaan bindu parr kendrit ack gausi vitaran kaa upayog kartaa haye. yeh prastaav vitaran namuna lene key liye suvidhajanak haye aur yadi kissy koo lakshya vitaran, sootra _ 2 key baare mein bahut cumm gyaan haye tou yeh sabse achchha vikalp hoe sakata haye. yadi vaanchhit haye, tou koee adhik samanya bahubhinnata samanya vitaran, sootra _ 3 kaa upayog curr sakata haye, jahaan sootra _ 4 sahprasaran matricks haye joe upayogkarta kaa maanana haye kii lakshya vitaran key samaan haye.
haalaanki iss vidhi koo anant namuna aakar kii seema mein sthir vitaran mein parivartit honah chaahiye, vyavhaar mein pragati bahut dheemi hoe sakati haye. yadi sootra _ 5 bahut badaa haye, tou aim. aich. algorithm key tahat lagbhag sabhi charanon koo aswikar curr diyaa jaayega. doosari or, yadi sootra _ 5 bahut chhota haye, tou lagbhag sabhi charanon koo sweekaar curr liya jaayega, aur markov shrinkhala sambhaavyata sthaan key madhyam seey yaadrichhik chalane key samaan hogi. sootra _ 7 key saral mamle mein, humm dekhate hain kii sootra _ 8 kadam kewal hamein sootra _ 9 kii doori taka leey jaate hain. iss ghatana mein, markov shrinkhala kissy bhee uchit samay mein sambhavana sthaan kaa poori tarah seey pataa naheen lagaayegi. iss prakaar aim. aich. algorithm key liye paimaane key mapdand (sootra _ 5 yaa sootra _ 4) key uchit tuning kii aavashyakta hoti haye.
uchch ayamita key saath samasyaaen.
bhale hii paimaane kaa mapdand achchi tarah seey tune kiya gayaa hoe, jaise-jaise samasya kii ayamita badhati haye, pragati abhee bhee bahut dheemi reh sakati haye. ise dekhane key liye, phir seey sootra _ 7 parr vichaar karein. ack ayam mein, yeh maadhya 0 aur vicharan 1 key saath ack gausi vitaran seey mell khaata haye. ack ayam key liye, iss vitaran mein shoonya kaa ack maadhya charan haye, halanki maadhya varg charan aakar dwara diyaa gayaa haye
jaise-jaise aayamon kii sankhya badhati haye, apekshit charan kaa aakar badaa aur badaa hoe jaataa haye. sootra _ 8 aayamon mein, ack radial doori sootra _ 15 koo sthanantarit karane kii sambhavana chee vitaran seey sambandhit haye, aur isake dwara dee jaati haye
yeh vitaran sootra _ 17 parr charam parr haye joe badey sootra _ 8 key liye sootra _ 18 haye. iska matlab haye kii charan kaa aakar aayamon kii sankhya key motey taur parr vargamool key roop mein badhega. aim. aich. algorithm key liye, badey kadam lagbhag hamesha cumm sambhavana vaale kshetron mein utarenge, aur isaliye aswikar curr diye jaayenge.
yadi abb humm paimaane key mapdand sootra koo jodate hain, tou humm paate hain kii ack uchit sweekriti darr koo banaae rakhane key liye, hamein parivartan sootra _ 21 banaana hoga. iss sthiti mein, sweekriti darr koo abb uchit banaaya jaa sakata haye, lekin sambhavana sthaan kaa anveshan teji seey dheema hoe jaataa haye. ise dekhane key liye, samasya key kissy bhee ack ayam key saath ack tukade parr vichaar karein. oopar key paimaane koo parivartit karke, apekshit charan kaa aakar koee ack ayam haye joe sootra _ 22 naheen haye, balki sootra _ 23 haye. kyonki yeh charan aakar sambhaavyata vitaran key "sahee" paimaane seey bahut chhota haye (yeh maanate hue kii sootra _ 22 kissy tarah seey ack prathamikta haye, joe sabse achchha sambhav mamla haye), algorithm pratyek parameter key saath ack yaadrichhik chalane koo nishpaadit kartaa haye.
ekaadhik-prayaas mahanagar algorithm.
maan leejiye kii sootra _ 25 ack manmana prastaav kaary haye. hamein usa sootra _ 26 kii aavashyakta kewal tabhi hoti haye jaba sootra _ 27. isake atirikt, sootra _ 28 sambhaavyata kaary haye.
sootra _ 29 koo paribhaashit karein jahan sootra _ 30 sootra _ 31 aur sootra _ 32 mein ack gair-nakaratmak samamit kaary haye jise upayogkarta dwara chunaa jaa sakata haye.
abb maan leejiye kii vartamaan sthiti sootra _ 31 haye. aim. tii. aim. algorithm iss prakaar haih
1) sootra _ 35 seey "key" swatantra pareekshan prastaav sootra _ 34 banaaen. inmein seey pratyek key liye bhaar sootra _ 36 kii ganana karein.
2) sootra seey sootra kaa chayan karein _ 38 vajan key aanupaatik sambhavana key saath.
3) abb vitaran sootra _ 40 seey sootra _ 39 kheenchkar ack sandarbh sett kaa utpaadan karein. sootra _ 41 (vartamaan bindu) nirdhaarit karein.
4) sambhavana key saath sootra _ 32 sweekaar karein
yeh dikhaaya jaa sakata haye kii yeh vidhi vistrit santulan guna koo santusht karati haye aur isaliye sthir vitaran key roop mein sootra _ 28 key saath ack prativarti markov shrinkhala kaa utpaadan karati haye.
yadi sootra _ 25 samamit haye (jaisa kii bahubhinnata samanya vitaran key liye haye), tou koee sootra _ 46 chuna sakata haye joe sootra _ 47 detaa haye.
nuksan.
kaee-prayaas mahanagaron koo pratyek charan mein sootra-48 anya avasthaon kii oorjaa kii ganana karane kii aavashyakta hoti haye.
yadi prakriya kaa dheema hissa oorjaa kii ganana curr rhaa haye, tou yeh vidhi dheemi hoe sakati haye.
yadi prakriya kaa dheema hissa kissy diye gaye bindu key padosiyon koo dhoondh rhaa haye, yaa yaadrichhik sankhya utpann curr rhaa haye, tou phir seey yeh vidhi dheemi hoe sakati haye.
yeh tark diyaa jaa sakata haye kii yeh vidhi kewal teji seey dikhaai detee haye kyonki yeh mahanagar-shikaar kii tulanaa mein "ekal charan" mein bahut adhik ganana karati haye.

