Parallel Radix Sort by Using MPI

Q~j l t7 @i @i mp ~ql tb _l _l ulhnh Antlbk Antlbk & Bm phn mn kql tb Ul Ul a bs Tiuq _l ul hhnh hhnh Zl rl k Tubrlt Tubrltl l ) J6>1 J6>1

_lulhhnh Ulabs Tiuq7 Bmphnmn kql kql tb Ankjl Ankjl k Mn kjj~k`l kjj~k`l k M_B M_B _nkalc~h~lk _nkj~u~qlk) tiuqbkj _nkj~u~qlk) tiuqbkj al al ql m nu~pl nu~pl `lk ip nultb nultb rlkj rlkj tlkjl q ~m~m a bhl`~`lk l`~`lk ihnc ihnc ìmp ~qnu `lunkl `lunkl a lql rlkj qn u~u u~u~q hnebc hnebc m~al c abpuitnt abpuitnt al ubpla l a lql rlkj m l tbc ldl` Ti uqbkj uqbk j aba nfbkbt nfbkbtb`lk b`lk tne l jb tne tne ~l c qlt` ~kq~` qlt` ~kq~` mn kjl q~u tn`~mp ~hlk ~hlk al ql rlkj qnut~t qnut~t~k ~k tnd tnd l ul l d l` tncbkjj tncbkjj l abcl tbh`lk bh`lk t~t t~t~kl ~kl k rlkj qnu~u~q qnu~u~q tnt tnt~l ~l b a nkj l k nhnm nk krl #al ub rlkj `nd bh `n `n e ntlu ntlu lql ~ tne tne lhb`krl" lhb`krl" Mn m-pl ulhhnh ulhhnh-` -`lk lk tne tne ~lc l hjiubqm hjiubqm l tn| ~nkd blh ti ti uqbkj mn qbkj mn hbel q`lk pn kabtqub kabtqube~t e~tblk blk nhnmnk rlkj l`lk a b~u b~u~q`lk `npl al puitnt puitntiu iu rlkj qn utnabl  Lal en en ul pl clh rlkj clu~t abpn uclqb`lk( rlbq~7 rlbq~7 < abmlkl qnmp lq p nkrbmplklk nkrbmplklk bkp~q bkp~q al k i~qp~q bqm l tn`~nkt tn`~nktblh blh puitnt puitnt bkb an kjl k dn pl q al pl q abhl`~`lk abhl`~`lk cl krl i pl al lhji ubqm ankj lk m nkjj ~kl`lk mnm iub iub hi`lh hi`lhkrl krl i pl al lhji ubqm bqm l p lulhhnh( lulhhnh( gb`l gb`l nhnmnk qn uhnql` pl al p uitnt itnt hi`l hi`l h m l`l l `lk mnkglab d ~`~p ~`~p m ~al c tna tna lkj`lk gb`l gb`l nhnmnk nhnmnk enulal pl al puitnt puitnt rlkj enuena l m l`l l `l k mnkglab hnebc hnebc u~mbq u~mbq 5 Elj lbml kl p uitnt uitnt pn me lka bkjl bkjl k abhl`~`lk abhl`~`lk ihnc lhjiubqml lhjiubqml i Tl q~ nhnm nk p nu puitnt puitnt i Hne bc al ub tlq tlq ~ nhnm nk pn u p uitnt itnt Lhji ubqm ubqm l Ul a bsT bsTi uq _l _l ulhhnh Lhji Lhji ubqml Ul abs Tiuq abe~l q a nkj lk m nkj j~kl `lk unpuntnkql unpuntnkql tb ebknu ebhlkj ebhlkj lk rlkj l`l k ab-tiuq ab-tiuq Gb`l Gb`l m btlhkrl btlhkrl e mnu~pl `lk g~mhlc g~mhlc ebq pl al ebhlkjl k ml `l ula ula bs tiuq iuq l`lk mnhl`~`lk puitnt tiuqbkj qnuclalp u ebq tnqblp tnqblp z l`q~( abml kl u 8 e Tncbkjj l ula bs tiuq l`lk mn hl`~`lk hl`~`lk tne lkrl ` e) u bqnultb bqnultb Tnhlm l bqn ultb ltb `n `n -b( -b( l`l k a bhl`~`l bhl`~`l k p nkj ~u~ql ~u~ql k ebhlkj l k tnt tnt~lb ~lb a n kjl k e bq HT HTE `n `n -b al ub u ehi` e bq bq Lhji Lhji ubqml pl ul hhnh ~kq~` ~kq~` lhjiubqml lhjiubqml ula bs tiuq la l hc tne tne lj lb e nub` nub`~q ~q #Lklkqc Julm Julm l( 5??4"7 < 5 4 1 > 6 : 3 2  <6 <: <3

puidna~un ULABS TIUQ#L( u" enjbk fiu b 7= ? qi e)u - < ai enjbk ifftnq 7= ?0 fiu g 7= ? qi 5 u - < ai enjbk fhlj 7= ?0 bf qcn b qc hnltq tbjkbfbdlkq u-ebq ehid` if LP_ `] = g qcnk fhlj 7= <0 bkans 7= punfbsYt~m#fhlj" punfbsYt~m#fhlj" bf fhlj = < qcnk ulk` 7= ifftnq + bkans0 ifftnq 7= plulhhnhYt~m#fhlj"0 plulhhnhYt~m#fhlj"0 nkafiu nldc puidntt _` tnka bqt nhnmnkq LP_ `] qi puidntt _ ulk`0 nkafiu nka ULABSYTIUQ

Tnhlm l bqn ultb ltb al ub hii hii p p l al e lubt 6-<> 6-<>(( uula la bs tiuq m nknk q~`lk p itbt itbtbb nhnm nhnm nk an kj lk kbhlb u ebq al ub g _nucbq~k nucbq~kj j lk bkb abhl`~`lk abhl`~`lk an kjl k mnkg~mhlc`lk tnm~ tnm~ l nhnmn k an kjl k kbhlb kbhlb rlkj tlm l al k `nm~a blk mn kjbubm`lkkrl kjbubm`lkkrl `n puitnt puitntiu iu Vlublehn Vlublehn ulk` mnu~pl`lk <

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pn kl kal p itbt itbtbb tnqbl tnqbl p nhnm nk( abl `cbu `cbu hii hii p #el ubt <6"( <6"( tnq tnq blp p uitnt itnt m nkj bubm`lk bubm`lk nhnm nkkrl `n p uitnt itntiu iu _ulk` Alhlm bmphnm nkqltbk nkqltbkrl rl lhji ubqml bkb bkb al p lq abhl`~`lk abhl`~`lk ankj lk p nkan `lqlk d i~kqbkj i~kqbkj tiu tiuqq lql ~ e~d `nq tiuq tiuq Antlbk Antlbk Ankj lk M nqia n Fitqnu itqnu < _luqbqbikbkj Gnkbt Gnkbt pl uqbqbikbkj qbqbikbkj rlkj abhl`~`lk abhl`~`lk p la l a ntlbk ntlbk lhji ubqm bqm l bkb la lhlc a lql pl uqbqb qbqbikbkj( abmlkl al ql l`lk a bpnd lc m nkgla nkgla b tne tne lkrl` k) p al k ab`bu ab`bubm`lk `ntnqblp puitntiu 5 Dimm~kbdlqbik _uitnt itnt ìm ìm ~kb`lt ~kb`ltbb rlk j qnugla b lkql ul hl bk7  Td lq qnu( abhl`~`l abhl`~`l k ~kq~` mn kjbub kjbubm `lk k) p n hnmn k `ntnqblp `ntnqblp p uitnt itntiu iu thlvn thlvn   Jl qcnu( abhl`~`l abhl`~`l k ~kq~` mn kjbub kjbubm `lk cl tbh pn kj~ u~ql k `n p uitn itn tiu m ltqnu ltqnu  Tnka & und nbvn( a bhl`~`l bhl`~`l k ~kq~` m nkj bub bubm `lk bkfium bkfium l tb en tlu luul luul r rlkj l`lk abhl`~`lk abhl`~`lk hi`lh hi`lh ìmp ~qltb ~qltb 4 Ljhimnulqbik _uitnt itnt lj jhim nultb nultb qn ugla b `nqb`l pn kjj le ~kjl k 5 t~e-l t~e-l uul r( al k mn kj ~u~q`l ~u~q`l kkrl `nm el hb `n `n p uitnt itntiu iu hlbk 1 Mlppbkj Ml p pbkj abhl`~`lk abhl`~`lk `nqb`l a lql rlkj qnhlc ab-ljj him nultb nultb tblp tblp ab`bu ab`bubbm `n p uitnt itntiu iu qnuan`lq Bh~t Bh~tqult qultbb _nk _nk nul p l k Lhji ubqm ubqm l Ul abs Tiuq Tiuq Enub`~q nub`~q m nu~pl `lk bh~tqult bh~tqultbb pn knulp l k l hjiubqml ula bs tiuq 7 Bkp~q al ql 7

l  Bqnultb qnultb pnuqlml ~kq~` el jblk a bjbq bjbq tlq~l tlq~l k  M btlh`lk qnual p lq 5 p uitnt itntt tiu( al ql a bel jb mn kgl kgl a b 5 ~kq~` ml tbkj- m l tbkj p uitntti uitntti u 7 _? _<

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Mnkj~mp~h`lk fun`~nktb abjbq alub qblp puitnttiu `n puitnttiu ? Hid l h K~m K~m Bqnm 

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M nkj ~mp ~h`lk ~h`lk a lq l rl kj t~a lc qnu~u~q qnu~u~q a lub qbl qbl p p uitnt uitntt tiu `n `n p uitnt itntt tiu ? Qnm p Hid Hid lh Alql 

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Mnkj~u~q`lk alql rlkj t~alc qnu~u~q tndlul hi`lh alub qblp puitnttiu Hid l h K~m K~m Bqnm 


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e  Bqnultb `na~l ~kq~` abjbq p~h~clk






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Mn kj ~m p ~h`lk fun`~n ktb ktb abj bq a l ub qblp p uitnt uitntt tiu `n p uitntt uitnttiu iu ? Hid l h K~m K~m Bqnm 

Al ub _?

Al ub _<

Mn kj ~mp ~h`lk ~h`lk al ql rlkj t~al c qnu~u~q al ub qblp qblp p uitnt itntt tiu `n `n p uitnt itntt tiu ? Qnm p Hid Hid lh Alql 

Al ub _?

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Mnkj ~u~q`lk ~u~q`lk a lq l rlkj t~al c qn u~u~q ~u~q tnd tnd lul hi`lh hi`lh a lub qblp qblp puitnt puitntt tiu

Hid l h K~m K~m Bqnm









Alql qnhlc qn u~u~q ~u~q

Bmphnmnkqltb Lhjiubqml @nalhlm _uijulm Alhlm bmphnmnkqltbkrl( lhjiubqml bkb aban`lqb ankjlk mnkjj~kl`lk pn ka n`l ql k e~d `nq tnt tnt~l ~l b an kj lk bh~t bh~tqult qultbb abl ql t Tnd l ul `ntnh~u `ntnh~u~cl ~cl k puij ulm qnua bub al ub 4 f~kj f~kj tb rlkj m ltbk ltbkj-ml j-ml tbkj bkj en uf~kjtb f~kjtb ~kq~` pnkrna bl a lql ( tiuqb tiuqbkj kj p la l e~d `nq al k f~kjtb f~kjtb ~ql ml rlkj m nm lkj j bh `nqbjl f~kj tb qn utne ~q Enub`~q nub`~q anq lbh f~kj tb rlkj abml`t~a`lk7 F~kjtb E~lqAlql #hikj bkq P]( bkq( bkq( bkq" Tnel jl b bkp~q bkp~q a lql ( pla l puijulm puijulm abtnu abtnuql`lk ql`lk f~kjtb f~kjtb ~kq~` ~kq~` mnkjnknulqn e bhlkj lk l d l` tnelkrl` k e~l c e bhlkj bhlkj lk tnt~lb nt~lb an kjl k `nbkjbklk `nbkjbklk ~tnu ~tnu Ebhlkjl k l d l` a belkj `bq`lk `bq`lk an kjl k m nkjj ~kl`lk f~kj tb ULKA ULKA#" #" Enub`~ nub`~qq d ~phb`lk ~phb`lk f~kjtb f~kjtb ~kq~` mn me ~lq a lql bkp~q7 bkp~q7 )'''''''''''''''''''''''''''''''''''''''' )'''''''''''''''''''''''''' '''''''''''''''''''''''''''' ''''''''''''''''''''''''') ''''''''''') viba E~lqAlql#hikj E~lqAlql#hikj bkq luulrY~qlmlP] )' i~q ')( ') ( bkq k )' bk ') ')( ( bkq kYplu )' bk ') ')( ( bkq p )' bk ') ')" "  )' mnkrbmplk mnkrbmplk nhnmnk `nalhlm `nalhlm pnkrbmlk pnkrbmlk tnmnkqlul ') bkq b( |0 M_BYTqlq~t tqlq~t0 pubkqf#%Tnenh~m pubkqf#%Tnenh~m tiuqbkj7Xk%"0 tiuqbkj7Xk%"0 fiu #| = ?0 | 8 p0 |++"  pubkqf#%Xk_.a7 pubkqf#%Xk_.a7 %( % ( |"0






F~kjtb Tn|Ytiuq#hikj bkq P]( bkq" F~kj tb bkb bkb e nuq~jl t ~kq~` mnhl `~`l `~`l k tiuqb tiuqbuu pl a l e ~d `nq( enub`~q d~p hb`lk hb`lk ìa n puijulmkrl7 )'''''''''''''''''''''''''''''''''''''''' )'''''''''''''''''''''''''' '''''''''''''''''''''''''''' ''''''''''''''''''''''''') ''''''''''') viba Tn|Ytiuq#hikj Tn|Ytiuq#hikj bkq luulr luulrP] P] )' bk)i~q ')( ')( bkq tbwn )' bk ')" ') "  )' tiuq tiuq ankjlk ankjlk mnkjj~kl`lk mnkjj~kl`lk tnhndqbik tiuq ') bkq nffYtbwn( mbkpit0 hikj bkq qnmp0 fiu#nffYtbwn = tbwn0 nffYtbwn ; <0 nffYtbwn--"  fiu#nffYtbwn mbkpit = pitbtb#luulr pitbtb# luulr( ( nffYtbwn"0 qnmp = luulr luulrPmbkpit]0 Pmbkpit]0 luulrPmbkpit] luulr Pmbkpit] = luulr luulrPnffYtbwn-<]0 PnffYtbwn-<]0 luulrPnffYtbwn-<] luulr PnffYtbwn-<] = qnmp0 } } )' mnkjnmelhb`lk bkans nhnmnk qnu`ndbh `n `bub ') bkq pitbtb#hikj pitbtb#hikj bkq luulr luulrP]( P]( bkq nffYtbwn"  bkq b( mbkpit = ?0 fiu #b=?0 b8nffYtbwn0 b++" mbkpit = luulr luulrPb] Pb] ; luulr luulrPmbkpit] Pmbkpit] 9 b7 mbkpit0 unq~uk mbkpit0 } )'''''''''''''''''''''''''' )'''''''''''' '''''''''''''''''''''''''''' '''''''''''''''''''''''''''' ''''''''''''''''''''''''') ''''''''''')

Lhji Lhji ubqm bqm l tiuqbkj iuqbkj rlkj abj~kl `lk p la l f~kjtb f~kjtb bkb bkb la lhlc lhji ubqml tn| ~nktblh ~nktblh tiuq( tiuq( an kjl k l t~mtb ~mtb el czl lhji ubqml qnutne qnutne ~q m nmbhb` nmbhb`bb tqle tqle bhbqlt bhbqlt rlkj d ~`~p e lb` lb` F~kjtb mlbk #bkq lujd ( dcl u' lujvP]" F~kj tb ~ql m l bkb mn hl`~`lk p uitnt itnt pl ul hnhbt hnhbtlt ltbb tnd lul ~q~c ( m ~hlb al ub p nm e ~l ql k al ql ( pn krnel ulk `n tnqblp tnqblp puitnt puitntiu iu tlm tlm pl b ank jl k m nj~m p~h`lk `nme lhb cltbh cltbh tiuqbkj iuqbkj rlkj






luulrY~qlml = mlhhid#k'tbwnif mlhhid#k' tbwnif# #hikj bkq bkq""0 ""0 bf #mrYulk` == ?"  tqluq = M_BYZqbmn#"0 )' Qbmbkj ') )' ~kq~` dn` `nhbplqlk nhnmnk ankjlk g~mhlc puitntiu ') bf #k.p ,= ?"  fpubkqf#tqanuu(%G~mhlc fpubkqf#tqanuu( %G~mhlc nhnmnk e~`lk `nhbplqlk g~mhlc puitntiuXk%"0 puitntiuXk% "0 M_BYLeiuq# M_BYDIMMYZIUHA( M_BYDIMMYZIUHA( 5 "0 nsbq#<"0 } )' mnme~lq luulr ~kq~` mnklmp~kj tnm~l alql ') bf #luulrY~qlml==K^HH" #luulrY~qlml==K^HH"  fpubkqf#tqanuu( %lhi`ltb mnmiub luulrY~qlml jljlh,,Xk% "0 M_BYLeiuq# M_BYDIMMYZIUHA( M_BYDIMMYZIUHA( 4 "0 nsbq#?"0 } pubkqf#%XkQiqlh pubkqf#%XkQiqlh nhnmnk = .a0 Xk%( Xk% ( k"0 E~lqAlql#luulrY~qlml( k( k)p( p"0 } kYplu = k)p0 luulrYhi`lh = mlhhid#kYplu'tbwnif mlhhid#kYplu'tbwnif# #hikj bkq bkq""0 ""0 bf #luulrYhi`lh==K^HH" #luulrYhi`lh==K^HH"  fpubkqf#tqanuu( %lhi`ltb mnmiub luulrYhi`lh jljlh,,Xk% "0 M_BYLeiuq# M_BYDIMMYZIUHA( M_BYDIMMYZIUHA( 1 "0 nsbq#?"0 } )' mnkrnelu`lk mnkrnelu`lk nhnmnk alql rlkj lal plal luulrY~qlml `n tnqblp puitntiu M_BYTdlqqnu#luulrY~qlml( M_BYTdlqqnu#luulrY~qlml( kYplu( M_BYHIKJ( luulrYhi`lh( kYplu( M_BYHIKJ( ?( M_BYDIMMYZIUHA"0 M_BYDIMMYZIUHA"0 Tn|Ytiuq#luulrYhi`lh( Tn|Ytiuq#luulrYhi`lh( kYplu"0 M_BYJlqcnu#luulrYhi`lh( M_BYJlqcnu#luulrYhi`lh( kYplu( M_BYHIKJ( luulrY~qlml( kYplu( M_BYHIKJ( ?( M_BYDIMMYZIUHA"0 M_BYDIMMYZIUHA"0 tqip = M_BYZqbmn#"0

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Enub`~q nub`~q cl tbh u~kkbkj ìa n p uij ulm abl ql t7

@i m p hn`tbql hn`tbql t( Tp Tp n na ~p ( Nfbt Nfbtbnktb bnktb al k Bt Btt tin fbtbnk fbtbnkt tb @im phn`tbqlt phn`tbqlt tn`~nk tn`~nk tblh al ub lhj iubqm iubqm l ul abs la l hlc Q = I#k"

Parallel Radix Sort by Using MPI

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