A Historical Analysis of Fiber Based Optical Bus Parallel Computing Models

AHISTORICAL ANALYSISOF FIBERBASED OPTICAL BUSPARALLEL COMPUTING

MODELS

BRIAN J. D'AURIOL

∗

AND MARIA BELTRAN

†

Abstrat. Aomprehensiveoverview andsurveyofthedevelopmentsinoptialbusparallelomputingmodelsispresented

inthispaper. Therstmodelproposedwasthe APPBin1990. Sinethen,intheorderoftheirappearane,theremainingnine

modelssurveyedare: APPBS, ASOS,LPB,RASOB,AROB,LARPBS,PB,LAPOBand PR-MESH.Researhtrends observed

fromthisanalysisindiateperiodsofmodeldevelopmentleadingtomoreand moresophistiationand omplexityinthe model,

followedbyperiodsofmodelsimpliations.Theseperiodsappearstoourinyles. Wenotethewidespreadandglobalresearh

interestinthese models. Thethreemostpopular modelsappeartobeRASOB,AROBand LARPBS.Wealsohaveanalyzeda

ruialaspetofthesemodels,thebusyletimedenitions,andhavedeterminedinauraiesinmostofthedenitionsappearing

intheliterature. Wealsoproviderenementtothedenitionstoorretsuhinauraies.

Keywords. OptialBus,ParallelComputing

1. Introdution. Optialberbusinteronnetionparallelomputingmodelswereinitiallyproposedover

adeadeago. Sinethen,atleasttendistintmodelshavebeendevelopedwithmanyorrespondingpubliations.

Inaddition, related work on implementationas well asroutingand addressinghavebeen noted. A prinipal

reasonforthesuessofthisresearhareastemsfromtheadvantagesofoptialommuniationstogetherwith

bus-based systems. Some ofthe advantages inlude inherent pipelining ofmessagesdue to the unidiretional

propagationnatureofoptialsignalsaswellaspowerspeedandrosstalkadvantagesovereletronibuses[1℄.

A omprehensive overview and survey of the developments in optial bus parallel omputing models is

presented in this paper. This surveyinludes ten optialbus models that wereproposed between theperiod

of1990 to 2000. Manypubliations haveappeared andpubliations ontinueto be submittedbasedonthese

models. First, adesription of thesalientparts of optial buses is given. Next, the tensurveyedmodels are

desribed. Observations regardingsimilarities anddierenes inherentin the models arenoted. Lastly, some

analytialommentsarepresented.

Several papersprovidesurvey-typeinformation. These surveypapers[2,1℄are notreportedin themodel

summarysetions. Thispaperatuallyextendstheworkoftheabovesurveypapers.

Thepurposesofthispaperarethree-fold. First,toprovidetotheomputerprofessionalswhodonothave

detailed knowledge of optial bus parallel models an introdution and overview of the major points of these

modelsaswellasprovidinginformationaboutthevariousproposedmodels. Seond,toprovidetotheresearh

ommunityahandy-refereneofrstitations,ategorizationsofexistingpubliationsandasoureofadditional

materialtoonsider. Third,toprovidetotheresearhommunityanextensiveliteraturebibliography.

The paper is organized as follows. A review of basi onepts in optial busparallel models is given in

Setion 2. In Setion 3, a brief overview of ten optial bus models with an emphasis on bus yle is given.

Historialomments are madein Setion 4. An analysis of bus yles denitions in these models is given in

Setion5. ConlusionsaregiveninSetion6

2. OptialBusModel. Ingeneral,anoptialbusmodelusesoneormoreoptialwaveguidestoonnet

alineararray of

N

proessorslabeled

0

through

N

−

1

. This arhitetureanbeextended to morethanone

dimensionwhere,forexample,proessorsarearrangedinamatrix. Proessorsareonnetedtothewaveguides

by injetors,whih injet light pulses onto the waveguide(s), and detetors, whih detet light pulses on the

waveguide(s). Thetimeittakesapulsetotraversethedistanebetweenanytwoadjaentinjetion points(or

twodetetionpoints)isaonstantommonlyreferredtoas

τ

,whilethedurationofthepulseisusuallyreferred

to as

ω

. In the literature, one simple ase of ollision is addressed by dening

b

as the maximum size of a

messagesuhthat

bω < τ

.

Therearefouraspetsofoptialbusmodelsthatmaybeusedasriteriaforlassiation: (1)thenumber

of buses to whih proessorsare onneted, (2) the type of bus that is used (folded or non-folded), (3) the

dimensionofthemodel, and(4)thetypeofaddressingused. These aspetsaredetailedbelow.

Inorderto enableallproessorsarrangedinalineararrayto ommuniatewitheahother, the

interon-netionnetwork mustallowtra totravelin twodiretions. Dueto theunidiretionalpropagationproperty

∗

(dauriolam.org).

†

τ

3

P

_N

p

P

1

P

pulse

dectectors

pulse

injectors

2

Fig.2.1.Non-folded (Two)BusConguration

of light, however,asingleoptial busrunningalongthe lengthofthe arraywill onlyallow ommuniationin

onediretion. Thediretionalrequirementisfullledbyusingtwobuses. Figure2.1illustrates this. Notethat

proessorsare onneted to bothbuses by bothinjetors and detetors. The twobuses in this onguration

arereferredtoasnon-foldedbuses. Thefoldedbus,ontheotherhand,ombinesbothdiretionalrequirements

into a single bus. It is a single bus that parallels the array of proessors, and is folded around one of the

endsofthearray. Thisenableslightto travelinbothdiretionswith respettotheproessors. Typially,the

linearsegmentbeforethefold isalledthetransmittingsegmentwhilethatafterthefoldisalledthereeiving

segment. Onthetransmittingsegment,proessorsareonnetedbyinjetorsandonthereeivingsegment,by

detetors. Thetimeittakesapulsetotraversethefoldofthebusisaonstantthatisdenoted as

γ

,andisnot

neessarilyamultipleof either

τ

or

ω

. Figure2.2showsthefoldedbusarhiteture.

τ

pulse

dectectors

2

injectors

P

1

P

pulse

P

₀

P

_{N -1}

Fig.2.2. Folded(Single)BusConguration

Thisdesriptionoftheoptialbusarhitetureappliestoone-dimensional(or1-D)models. Thisarhiteture

is used as a building blok for models onsisting of more than one dimension. The most ommon

multi-dimensional modelfound intheliteratureisthe two-dimensional(or 2-D)model. Insuh amodel,proessors

are arranged in a matrix format and the optial buses belong to one of two groups, rows or olumns. The

orientationoftherowbusesisperpendiulartothatoftheolumnbuses. Thetwo-dimensionalmodelhasbeen

The literature searh indiates that, in models that use more than one waveguide, models with three

waveguidesarethemostommonlyusedonguration. Coinidentpulseaddressing,disussedsubsequently,is

theprimaryreasonwhythreewaveguidesareused. Mostofthemodelsthatemploymorethanonewaveguide

provideoneforthemessageand theremainingtwoforaddressingpurposes. Thetwoaddressingwaveguidesit

usesarereferredtoastheseletandreferenewaveguides.

Coinident pulse(CP) isthe mostommonform of addressing. Delays ofduration

ω

are plaedbetween

everypairofdetetorsontherefereneandmessagewaveguidestoimplementCP.Addressingworksasfollows:

rst,thesoureproessorsendsapulseonthereferenewaveguideatthesametimeitstartstosendthemessage

onthemessagewaveguide. Then theproessorwaits afator of

ω

, depending on thedestination proessorit

wishesto ommuniate with, to send apulse on theselet waveguide. Thepulse on the referenewaveguide

is delayed by the delays on the reeiving segment suh that it will be deteted by the intended destination

proessoratthe sametimeastheselet pulse. At that pointthe message,whih also arrivesat the intended

proessoratthesametimeastheseletandreferenepulses,isreadinfromthemessagewaveguide. Figure2.3

showsafolded buswiththeoinidentpulseaddressingomponents.

pulse

pulse

injectors

pulse

dectectors

Select

Reference

Message

N -1

delay

P

0

1

P

2

P

P

τ

Permanent delay

Legend

Fig.2.3.Folded BuswithCoinidentPulse

Theotherommonly usedaddressingmethod istime-division multiplexing (TDM). This methodinvolves

assigningapartiulartimeslotforapartiularproessor. Thistimeslotaneitherbeusedtosend(time-division

souremultiplexing, orTDSM) orreeive(time-division destination multiplexing, orTDDM) optial signals.

Moredetailregardingthese busaspetsanbefoundin[2,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17℄.

Thenextsetionbrieydesribesthevariousbusmodelsfoundintheliterature. Apointofinterestineah

setionistheinformationregardingtheuseoftheterm`busyle'. Asubsequentsetionritiques theoverall

useofthisterm.

3. OptialBusesintheLiterature. Thissetionsurveystenoptialbusmodelsfoundintheliterature.

Therstonewasproposedin1990whilethelastin1998. Figure3.1depitstheoptialbusmodeldevelopment

inatimeline.

APPB

1993

1990

APPBS

1994

RASOB

LPB

ASOS

AROB

1995

LARPBS

1996

POB

1997

LAPOB

PR−MESH

1998

3.1. APPB(1990). TherstproposedoptialbusmodelistheArrayofProessorswithPipelinedBuses

(APPB)[3℄,whihanbeoneortwodimensions. Inonedimension,therearetwooptialbusesthatareplaed

paralleltoandoneithersideofalineararrayof

N

proessors. Eahproessorisonnetedtoeahbusviaone injetorand one detetor. This allowsa proessorto ommuniate with anyother proessor. Thebus yle

timeis

N τ

timeunits. Intwodimensions,eahproessorisonnetedtofourbusesbyaswith,tworowbuses

andtwoolumnbuses. Forthisonguration,abusyleisdenedas

N

1

τ

forarowbusand

N

2

τ

foraolumn

bus. Inaddition, theauthorsdene apetit bus yle as

τ

. APPB useseither TDMorCP foraddressingand

routing. Forthe TDMmethod in theonedimensional onguration, aset oftwoontrol funtions,send and

wait, areusedto ontrol aessto theoptialbus. Thetwodimensional APPBadapts thesendandwait and

introduestherelay funtion to provideontrol of messagesbetweendierentrows(messages travelrow-wise

rst). Figure 3.2 illustrates the one dimension arhiteture, while Figure 3.3 illustrates the two-dimensional

arhiteture. Individual waveguides are not shown. Rather, the optial bus is represented by a single line.

Variationsof APPB that inorporatefolded bus and onditional delay swithesare disussed in [18℄. Papers

reportingworkonAPPBare[3,19,20, 21, 22,23,24,25,26,27℄.

τ

3

P

_N

p

P

1

P

pulse

dectectors

pulse

injectors

2

Fig.3.2.APPB1-DArhiteture

3.2. APPBS (1990). TheArrayofProessorswithPipelinedBuses UsingSwithes(APPBS) [3℄ isthe

sameasthe2-DAPPB; with oneimportant dierene. Inthismodel, swithesareused at everyintersetion

of row and olumn buses, thus, eliminating the need for proessors to at as relays between the buses. As

with the APPB, APPBS an use TDMor CP addressingmethods and the bus yle is

(

N

1

+

N

2

)

τ

. Swith ongurationsimpattheommuniation. Eahoftheswithesanbeonguredasstraightorrossedandan

bedynamiallyreonguredrelativetothestartofthebusyle(byusingpetityles). Thisexibilityrequires

additionalonditionstoensureollision-freeommuniation,espeially whenmessagesneedtobeswithed at

the same plae and time. Algorithms suh asmatrix transpose, binary tree routing, and perfet shue are

implemented in a one step operation. This one step not only inludes bus yle time but also the time to

proesssomemessagesandtheswithsetuptime. Figure3.4illustratesthis model. Individualwaveguidesare

notshown. PapersreportingonAPPBSare[3,20,23,24,28,29℄.

3.3. ASOS (1993). TheArrayStruturewithSynhronousOptialSwithes(ASOS)[4℄isa

two-dimen-sionalmodel that uses multiple folded buses. This type of arhiteture onsists of asingle waveguidefolded

arounda lineararrayof

N

proessors. A

2

×

2

swith is plaedat the intersetions of reeivingsegments of

row buses and transmittingsegmentsof olumn buses. Eah proessoris onneted to the transmitting and

reeivingsegmentsoftherowbus,but onlyonnetedtothereeivingsegmentof theolumnbus. ASOSuses

a ombination of TDSM and TDDM to route messagesbetween rows and olumns; and the CP method for

destination addressing. Theterm busyle is notexpliitlymentioned, however, theend-to-end propagation

delayofarowbusismentionedandisdenedas

(2

N

−

1)

D

(where

D

roughlyorrespondswiththe

τ

elsewhere).

Fig.3.3. APPB2-DArhiteture

Legend

Switch

Fig.3.4.APPBSArhiteture

to the bus ontentionthat ours if morethan one proessor sends a message to the same olumn bus. To

alleviatethis,areservationwaveguideisinludedineahrowbus. Proessorsneedingtosendmessagesusethis

waveguidetodetermineiftherealreadyisamessagethatwouldontendwiththeirs. Priorityshemesareused

toestablishonitresolution. Figure3.5illustratesthisarhiteture. Individualwaveguidesarenotshown. A

Legend

Switch

Fig.3.5.ASOSArhiteture

3.4. LPB (1994). TheLinearPipelined Bus(LPB)modelappearsin 1994in [8℄. Thereissome

ontra-ditingevideneintheliteraturepertainingtothedenition andoriginoftheLPBmodel. Theauthorsof[28℄

ite[31℄,whihhassimilartitle,asasoureforthisoptialbusmodel. However,uponareviewofthatpaper,it

isonludedthat theontentdoesnotinlude optialbuses. Itispossiblethat theauthorsinadvertentlyited

the 1995 paper insteadof the 1994 paper. Theauthor of [32℄ ites referene #59, asubmitted paper asthe

soureforLPB,yetthat paperwasnotpublishedasited. It ispossiblethat, inreality,thatsubmittedpaper

is[33℄(whih hasadierenttitle but thesameauthors,albeit,in adierentorder). Personal ommuniation

withtheauthorof[32℄onrmsthatthesubmittedpaperwasindeedpublishedbut underadierenttitle and

dierent author order. In[33℄, the authorsite the1994 paperasthe soure ofLPB. Hene,it is onluded

thatthe1994publiation[8℄istheoriginalsoureofLPB.

LPBisaone-dimensionalmodelthat usesthefoldedbus. Itnotonlyhasthexeddelaysonthereeiving

segmentsoftherefereneandmessagewaveguides,butalsohasonditionaldelaysbetweeneverypairofinjetion

points on the selet waveguide. A busyle is dened as the end-to-end propagation delay on the bus and

is presented priorto inluding theuse of onditional delays(whih make theend-to-end propagation delaya

variable). Thebusyleformulaisdenedas

2

N τ

+(

N

−

1)

ω

. Figure3.6illustratesthisarhiteture. Individual waveguides are shown, inluding the plaement of delays.

S

1

, . . . , S

N

₋

₁

denote the onditional delays, eah

ontrolledbyproessors

P

1

, . . . , P

N

₋

₁

,respetively. WenotethesimilaritywiththeLARPBSmodeldesribed

later;inomparison,thismodelisnotreongurableandusesaslightlydierentaddressingtehnique. Papers

reportingonLPBare[8,34,33,31℄.

3.5. RASOB(1995). TheReongurableArraywithSpanning(orSlotted)OptialBuses(RASOB)[5℄

is similar to ASOS.The arhiteture was initially designed to support SIMD proessing and to ontain less

omplexities than ASOS. It uses the folded bus, and an be one or two dimensional. In the former, eah

proessor is onneted to the bus on the transmittingand reeiving sides. In the latter, there is an

N

×

N

matrixoffolded buses. Asin ASOS,one

2

×

2

swith isplaedat eah intersetionof rowandolumn buses.

Eahproessorisonnetedtothebuses: twoonnetionsforreeiving(one forrow,oneforolumn)andone

fortransmitting. Aonstraintthatnomorethanoneproessorperrowansendamessagetoproessorsinthe

sameolumnexists in aommuniationyle. EitheraTDDM orTDSM methodis usedforaddressing. The

authors state that support for MIMD proessing ould be aomplishedby using oinident pulses, however,

pulse

injectors

pulse

dectectors

Select

Reference

Message

N -1

1

S

S

₂

S

_N

pulse

delay

Legend

Functional Control Circuit

Permanent delay

Conditional delay

P

0

1

P

2

P

P

-1

Fig.3.6. LPBArhiteture

bushas

2

N τ

yletime. Figure3.7 illustratesthisarhiteture. Thegureshowsa

3

×

3

RASOB.Individual

waveguidesarenotshown. PapersthatreportonRASOBare[5,35,36,37,38,39,40,41,42,43℄.

Legend

Switch

Fig.3.7.RASOBArhiteture

3.6. AROB(1995). TheArraywithReongurableOptial Buses(AROB)[6℄alsousesthefolded bus.

The AROB is an

N

1

×

N

2

reongurable mesh where eah proessor ontains registers for the temporary

storageof messagesbeingrouted. Proessorsusean internal swithing systemto reongure thenetwork by

onnetingor disonneting four I/Oports to eah other. Twoof the ports areonneted to either segment

of therow buswhile theother twoports are onnetedto the olumn bus. Both TDMand CP anbeused

greater than the end-to-end propagation time, the proessing time order must beof the samemagnitude as

thatof theend-to-endpropagationtime: thisisahievedbytheonditionthatthenumberofproessorsmust

begreaterthantheratiooftheproessingtimetoommuniationtime(subjettoanappropriatebuslength).

Twootherfeatures oftheAROB areitsbit pollingapabilityanditsapabilitytointrodue/adjustsignalsby

multipleunitdelaysperproessor[28,33℄. Bitpollingistheabilitytoseletthek th

bitofagroupofmessages

anddeterminethenumberofonebits. Figure3.8illustratesthisarhiteture. Thegureshowsa

3

×

3

AROB.

Individual waveguidesarenotshown. Papersthat report workonAROBare [6,25,44,45, 46,47,48,49, 50,

51,52,53,54,55,56,57,58, 59,60,29,28,61,62℄.

A

1

×

N

(one-dimensional) AROB isommonly referredto asaLinearAROBorLAROB. Thebusyle

time for LAROB is dened slightly dierently in dierent papers. In [6℄ it is dened to be the end-to-end

propagation delay:

2

N τ

plus some proessing time. In [57℄, it is dened slightly dierently, to be only the

end-to-endpropagation delay:

2

N τ

. Eah proessorontrolsits pairofbusonnetion swithes. When these

swithesare set rossedat aproessor,the bus issplit into twoat that point. In [60℄, AROB isextended to

multi-dimensions.

Fig.3.8.AROBArhiteture

3.7. LARPBS(1996). TheLinearArraywithaReongurablePipelinedBusSystem(LARPBS)[63℄is

aonedimensional reongurablefolded busmodel. Itontains

N

−

1

xeddelaysonthereeivingsideofthe

refereneandmessagewaveguidesand

N

−

1

onditionaldelaysonthetransmittingsideoftheseletwaveguide.

Swithes allow partitioning of the bus. Addressing an be done by either TDM or CP. Thebus yle is the

end-to-endpropagationdelayonthebus:

2

N τ

+

(

N

−

1)

ω

. UnlikeAROB, LARPBSdoesnotallowounting byproessors. However,atthebeginningofabusyle,eahproessormustset theonditionalswithes. Due

tothis (andotherfators),theauthorslaimthat LARPBS,unliketheoretialmodelssuhasPRAM,anbe

pratially implemented by urrent (as of 1996) optial tehnology. Refer to [64℄ for aurrent disussion on

implementationtehnology. Figure3.9illustratesthisarhiteture. Individualwaveguidesareshown,inluding

theplaementofdelays.

S

1

...

S

N

−

1

denotetheonditionaldelays,eahontrolledbyproessors

P

1

, . . . , P

N

−

1

,

respetively.

B

t

i

and

B

r

i

,

0

≤

i

≤

N

−

2

, denotethepairof swithesontrolledby

P

i

whihpartition thebus.

PapersreportingonLARPBS are[63,65,9, 66,67,68,69,70,71,72,73,74,75,76,77,32,78, 79,80, 81,82,

34,83,33,84,85,86,87,88, 89,90,91,92,93,94,95,96,97,64,98,99,100,101,102,103,104℄.

3.8. POB(1997). ThePipelinedOptialBus(POB)[10℄modelisaone-dimensionalfoldedbusmodel. It

pulse

injectors

pulse

dectectors

Select

Reference

Message

N -1

1

S

S

₂

B

t

₀

B

t

₁

t

₂

B

r

₀

B

r

₁

B

r

₂

N -1

S

pulse

delay

Legend

Functional Control Circuit

Permanent delay

Conditional delay

P

0

1

P

2

P

P

B

Fig.3.9. LARPBSArhiteture

τ

pulse

injectors

pulse

dectectors

Select

Message

Reference

Conditional Delay

Legend

1

P

2

P

3

P

N

P

ω

Fig.3.10. POBArhiteture

as needed. Addressingis done with either TDSM orCP. There is a possibleproblem that may our when

a message and a oinident pulse arrive at a destination proessor at the same time: during the detetion

time interval for a oinidene pulse, partof the message ould have alreadypassed by. The oset message

transmissionsheme (OMTS)addressesthisproblembysendingthemessagealittleaftertheseletpulse(the

endofthepreviousmessagestreamisallowedtooverlapwiththenextsetofaddressingpulses). Thebusyle

timeisthetimethatitwouldtake

N

onseutivepaketslotstopropagatealongthebus. Thelengthofapaket

slotismeasuredintimeunits,i.e.,thelargerofthelengthofthemessageorthetotallengthofitsassoiated

sequeneofseletpulses: atmost

D

=

τ

units. Themodelisdesribedbytheauthorsasmorepowerful"than

APPBandmoreost-eetive"thanLARPBS.Figure3.10illustratesthisarhiteture. Individualwaveguides

areshown,inludingtheplaementofdelays. PapersthatreportonPOBare[10,105,15,34,33℄

3.9. LAPOB (1998). TheLinearArrayof Pipelined OptialBuses (LAPOB) [11℄ isaone-dimensional

foldedbusmodel. ItusestheCPaddressingtehnique. Besidesthexeddelaysonthereeivingsegment,there

τ

pulse

injectors

pulse

dectectors

Select

Reference

Message

N -1

delay

P

0

1

P

2

P

P

pulse

Permanent delay

Legend

Fig.3.11. LAPOBArhiteture

positions of the destination proessorsform one of two patterns: ontiguousinterval (a sequene of adjaent

proessors) orregularlyspaed. Theformulaforabus yleis notgivenin thepaper. Oneadvantageis that

reonguration hardware is unneeded and, beauseof this, the model is less omplex. Figure 3.11 illustrates

thisarhiteture. Individualwaveguidesareshown,inludingtheplaementofdelays.

3.10. PR-MESH (1998). The Pipelined Reongurable Mesh (PR-Mesh) [7℄ uses the LARPBS as a

building blok to make up a

k

-dimensional mesh. The one dimensional PR-MESH is idential to LARPBS.

For the

k

dimension, eah proessorhas

2

k

ports onneted to buses. It uses the CP addressingtehnique.

The bus yle is desribedas the end-to-endpropagation delayas presented in APPB and LARPBS.In the

twodimensional mesh, eah proessorontrolsfoursets ofswithes,one set foreah intersetionof thebuses.

These swithes an beonguredin oneof ten dierent ways. This allows tra to owdierently between

a total of four dierent transmittingsegments and four dierent reeiving segments. Figure 3.12 illustrates

this arhiteture. Individual waveguidesareshown,inluding theplaementof delays. Papersthat report on

PR-MESH are[7,106,28,29℄.

4. Historial Analysis. Someanalysiswasonduted onthemodelsfoundintheliterature. Itinludes

observations about omparisonsbetween themodels, thetypes of algorithmsproposed,the popularityof the

models,trendsin arhitetureomplexityofthemodelsandsomemisellaneousobservationsofinterest.

Theoretialomparisonsbetweenseveral oftheoptialbusmodelsaswellaswithrespet toPRAMhave

beenpublished. Theseomparisonsseektoestablishboththefuntionalequivaleneandtherelativestrengths

of models. Several omparisons are reported in [6℄: AROB is ompared with reongurablenetworks; and,

APPB is omparedwith PRAM. LARPBS isompared with PRAM in [83℄. Theauthors in [7℄ omparethe

PR-MESHmodelwithotherreongurablemodelsonthebasisofomplexitylasses. Oneinterestingresultis

...theontributionofpipeliningtothe[PR-MESH℄modelislimitedtonomorethandupliatingbusesinthe

[LinearReongurableNetwork℄... TheequivaleneofLPB,POB,andLARPBSisreportedin[33℄. And,the

algorithm omplexities of thePR-Mesh, APPBS, and AROB are determined to besameas forthe LR-Mesh

and CF-LR-Mesh[29℄. Additional omparisonof the PR-MESH with the linearreongurablemesh appears

in[107℄. Somelimitedarhiteturalomparisonsarealsomadein[32℄.

Many of the papers surveyeddesribealgorithms forthe respetive models. In several ases, see for

ex-ample[6, 63, 32℄, ommuniationand omputationalgorithms aredeveloped asprimitivestobeused inmore

sophistiatedalgorithms. Theseinludebinaryprexsumsandompation. In[71℄,someoftheseprimitivesfor

theLARPBSmodelareformalizedinalemma. Ingeneral,algorithmsthathavebeendevelopedinludesorting

Conditional Delay

Permanent Delay

Switch

Legend

00

00

00

11

11

11

00

00

00

11

11

11

00

00

00

11

11

11

00

00

00

11

11

11

Processor

Fig.3.12. PR-MESHArhiteture(1Node)

taneTransform). Many algorithmsexhibit stati ommuniation deomposition,that is, theommuniation

pattern isstatiallydetermined during algorithm development. This isonsistent withboththealloation of

ommuniationintermsofbusylesaswellasalgorithmdevelopmentbasedonprimitiveoperations.

Trends were observed in the popularity of models aording to their level of omplexity. The analysis

inludedategorizingthe numberof publiationsreported permodeland peryear. Referto Table4.1for the

ompletelist ofmodelsand numberofpubliations. Injudgingtheomplexity, orsophistiation,of amodel,

thefollowingfeaturesare onsidered: multiple dimensionality,theuseofafolded bus,theuseofswithes,the

use of oinidentpulse addressing,and bus partitioning. The greater numberof these features that amodel

ontains,themoreomplexandsophistiateditisonsidered. Thisinformalriterionisusedtoguidethetrend

analysis.

From1990to 1993,aninreasein thesophistiationandomplexityoftheearlymodels isobserved. This

wasfollowedbyaperiod ofsimpliation (1993-1995). A jumpin thesophistiationisnotedin 1995withthe

AROBmodel. Again,aperiodofsimpliationfollows(1996-1998)withanotherjumpnotedforthePR-MESH

model. ItisnotedthatthisanalysisisonsistentwiththeintentionofRASOBasstatedinSetion3.5,thatis,

RASOBwasdesignedtohavefeweromplexitiesthanASOS.

The popularity of these models is observable from the number of publiations listed in Table 4.1 (some

publiationsareommontotwoormoremodels). Thethreemostpopularare: RASOB,AROBandLARPBS.

Combiningtheseresults,itissuggestedthatresearhersaremorestronglyattratedtosomethingbetween

thesimpleandtheompliated. Itis alsosuggestedthatthe apabilitiesinorporatedinto themodelsduring

themiddleperiod, 1995-1996,aresuientforsupportingurrentresearhinterests. Itisworthytopointout

thatthereentPR-MESH modelmayindeedsignify afutureresearh movementto onsidermodels ofhigher

degreesof sophistiationandomplexity. Ifso,thenthis mayalso indiatethat urrentresearhhasexplored

ModelPubliations

Model Numberof Year ofFirst

Publiations Publiation

APPB 10 1990

APPBS 6 1990

ASOS 1 1993

LPB 4 1994

RASOB 10 1995

AROB 23 1995

LARPBS 46 1996

POB 5 1997

LAPOB 1 1998

PR-MESH 4 1998

Perhapsin severalyears,additionalpubliationhistoryouldsupportorrefutesuhspeulation.

During the ourse of this analysis, several other interesting observations were noted. One publiation

reportingworkonASOSwasloated,yet,itisited inmanypubliations. Somepaperslaimthatto provide

for MIMD algorithms, additional omplexities would need to be inorporated. Other optial buses an be

foundintheliterature,forexample,freespaeoptialbusesaswellasNASA'sROBUSaspartoftheSPIDER

arhiteture. These modelsdo notappear tofollowthearhiteturalapproahof themodels surveyedin this

paperandthereforewerenotinludedintothispaper.

Somereentdevelopmentsare: a)therestritedLARPBS (RLARPBS)model[99℄proposedto more

au-ratelymodeltime analysisof algorithms, b)the parameterizedLARPBS (LARPBS(p)) model [103℄ proposed

asabridgingmodeland)agenerioptialbusmodel[108℄proposedtoapturesomeoftheommonfeatures

ofthemodelssurveyedinthispaperforMIMDommuniationanalysis.

5. Bus Cyle Issues. In theourseoftheanalysis,bus yleshavebeennotedto playaruial rolein

thealgorithmievaluationsonthesemodels. Inmanyases,algorithmomplexityisdesribedasorderOmega

of bus yle, for example, onstant time bus yle omplexity for the binary prex sums algorithm on the

LARPBS.Closerexaminationofbusyledenitionsonmanyofthemodelsrevealinonsisteniesbetweenthe

arhitetureandthedenition,thatis,thedenitionappearstorepresentasimplied arhiteture.

Investigat-ingthisfurther,itis notedthat nearlyallofthealgorithmiworkrefereningbusyleisgivenin theontext

ofasymptotianalysisexpressions,whereinonlythedominatetermneedstobeexpressed. Althoughnotinall

ases,itisnotedthatthedenitions asgivenintheliteratureareonsistentwithsuhause.

Arenementofthebusyledenitionsforallthemodelsispresentedinthissetion. Ageneralexpression

template is formulatedwhih is then applied to eah arhiteture. In general, the folded bus yle equation

isomposedof four parts. Part1of theequation orrespondsto thelengthof thetransmittingandreeiving

portionsof the folded bus. Part 2orresponds to theurvedportion ofthe bus,while Part 3orresponds to

thedelaysonthe bus. Part 4orresponds to theportionof thebus that remainspastthe detetionpoint of

thelast proessoronthe reeivingside of thebus. Reallfrom Setion2 that

bω < τ

. Toeiently usethe

bus bandwidth,

bω

should bemaximized. Tomodelthis requirement, thefator

τ

−

ǫ

is introdued, and may

beapproximatedassimply

τ

. Table5.1presentstherenedbusyledenitionsasomparedwiththosegiven

in the literaturefor eah of themodels. In theRened Bus Cyleolumn, `s', `r' and `m'referto the selet,

refereneandmessagewaveguides,respetively.

Notethat,in aseswherethemodelisonly2-D, oneof the1-D`piees'isusedto omputethebusyle;

in ases where the model is 1-D ormultidimensional, the1-D variety is used. On the PR-MESH, this is for

k

= 1

(the 1-Dase).

S

i

denotes eahof theonditional delays,where

S

i

= 0

meansthedelayontrolled by

P

i

isturnedoand

S

i

= 1

meansthedelayisturned on. Theproessortimeomponentis denotedby

φ

. For

Model Literature Rened Bus Cyle

BusCyle

APPB

N τ

(

N

+ 1)

τ

APPBS

N τ

(

N

+ 1)

τ

ASOS

2(

N

−

1)

τ

2(

N

−

1)

τ

+

γ

+

τ

+

φ

RASOB

2

N τ

2(

N

−

1)

τ

+

γ

+

τ

LPB

2

N τ

+ (

N

−

1)

ω

s:

2(

N

−

1)

τ

+

γ

+

ω

P

S

i

+

τ

r,m:

2(

N

−

1)

τ

+

γ

+ (

N

−

1)

ω

+

τ

AROB

2

N τ

+

φ

s:

2(

N

−

1)

τ

+

γ

+

τ

r,m:

2(

N

−

1)

τ

+

γ

+ (

N

−

1)

ω

+

τ

+

φ

LARPBS

2

N τ

+ (

N

−

1)

ω

s:

2(

N

−

1)

τ

+

γ

+

ω

P

S

i

+

τ

r,m:

2(

N

−

1)

τ

+

γ

+ (

N

−

1)

ω

+

τ

POB N/A s,m:

2(

N

−

1)

τ

+

γ

+

τ

r:

2(

N

−

1)

τ

+

γ

+

ω

P

S

i

+

τ

LAPOB N/A s:

2(

N

−

1)

τ

+

γ

+

τ

r,m:

2(

N

−

1)

τ

+

γ

+ (

N

−

1)

ω

+

τ

PR-MESH seeAPPB& s:

2(

N

−

1)

τ

+

γ

+

ω

P

S

i

+

τ

LARPBS r,m:

2(

N

−

1)

τ

+

γ

+ (

N

−

1)

ω

+

τ

6. Conlusions. Thispaperprovidesaomprehensiveoverviewandsurveyofthedevelopmentsinoptial

bus parallel omputing models. The rst model proposed was in 1990 and sine then, ten distint parallel

omputingmodelshavebeenproposed.

Speially,the researhtrends wehaveobservedindiate periodsof model developmentleadingto more

and more sophistiation and omplexity in the model, followed by periods of model simpliations. These

periods ourin yles. With the many publiations surveyed, we note the widespread and global researh

interestinthesemodels. ThethreemostpopularmodelsappearstobeRASOB,AROBandLARPBS.Wealso

haveanalyzedaruialaspetofthesemodels,thebusyletimedenitions. Wehavedeterminedinauraies

in most of the denitions appearing in theliterature, although, formost of the appliations suh denitions

havebeen used for, these inauraies appear notto be signiant. Inthe interests of larifying the orret

denitionsaswellastosupportoururrentresearhwork,wehavealsoprovidedrenementstothebusyle

denitions.

7. Aknowledgements. Muh ofthis workwasonduted whilethe authorswere at TheUniversity of

TexasatElPaso. WethanktheRefereneLibrarystaatKentStateUniversityfortheirassistaneinloating

itations.

REFERENCES

[1℄ S.Sahni,Modelsandalgorithmsforoptialandoptoeletroniparallelomputers,International JournalofFoundations

inComputerSiene,vol.12,pp.249264,June2001.

[2℄ S.Sahni,Modelsandalgorithmsforoptialandoptoeletroniparallelomputer,inpro.of1999InternationalSymposium

onParallel Arhiteture,AlgorithmsandNetworks(I-SPAN'99).,pp.27,June1999.

[3℄ Z.Guo,R.G.Melhem,R.W.Hall,D.M.Chiarulli,andS.P.Levitan,Arrayproessorswithpipelinedoptialbusses,in

Pro.3rd SymposiumonFrontiersof MassivelyParallel Computation(Cat. No.90CH2908-2)(J.Jaja,ed.),(College

Park,MD,USA),pp.333342,Otober1990.

[4℄ C.QiaoandR.G.Melhem,Time-divisionoptialommuniationsinmultiproessorarrays,IEEETransationson

Com-puters,vol.42,pp.577590,May1993.

[5℄ C.Qiao,Eientmatrixoperationsinareongurablearraywithspanningoptialbuses,inProeedings.Frontiers'95.

TheFifth Symposium ontheFrontiersofMassivelyParallel Computation(Cat.No.95TH8024). IEEEComput.So.

Press.1994,(MLean,VA,USA),pp.273280,Feb1995.

[6℄ S.PavelandS.G.Akl,Onthepower ofarrayswithreongurableoptialbuses, TehnialReport No.95-374,Queens

University,Kingston,Ontario,CANADA,February1995.

[8℄ Y.Pan,Orderstatistisonoptiallyinteronnetedmultiproessorsystems,OptisandLaserTehnology,vol.26,pp.281

287,August1994.

[9℄ Y. Pan and M. Hamdi,Quiksort on a lineararray witha reongurable pipelined bus system, inPro. of the IEEE

IntrnationalSymposiumonParallelArhitetures,Algorithms,andNetworks,pp.313319,June1996.

[10℄ Y.Li,Y.Pan,andS.Zheng,ApipelinedTDMoptialbuswithonditionaldelays,inProeedingsoftheFourth

Interna-tionalConfereneonMassivelyParallelProessingUsingOptialInteronnetions(J.Goodman,S.Hinton,T.Pinkston,

andE.Shenfeld,eds.),(Montreal,Canada),pp.196201,June1997.

[11℄ H.ElGindy,Animprovedsortingalgorithmforlineararrayswithoptialbuses(extendedabstrat),(Manusript),April

1998.

[12℄ D.M.Chiarulli,R.G.Melhem,andS.P.Levitan,Usingoinidentoptialpulsesforparallelmemoryaddressing, IEEE

Computer,vol.20,pp.4858,De.1987.

[13℄ S.Zheng,K.Li,Y.Pan,andM.C.Pinotti,Generalizedoinidentpulsetehniqueandnewaddressingshemesfor

time-divisionmultiplexingoptialbuses, Journal of Parallel and Distributed Computing, vol. 61, pp.10331051, August

2001.

[14℄ C.Qiao,R.G.Melhem,D.M.Chiarulli,andS.F.Levitan,Optialmultiastinginlineararrays,InternationalJournalof

OptialComputing,vol.2,pp.3148,April1991.

[15℄ S.ZhengandY.Li,Pipelinedasynhronoustime-divisionmultiplexingoptialbus,OptialEngineering,vol.36,pp.3392

3400,Deember1997.

[16℄ S.Zheng, ,and Y. Li, Apipelined TDM optial buswith improvedperformane, inProeedings. Third International

SymposiumonParallel Arhitetures, Algorithms, andNetworks(I-SPAN'97)(F.Lai,B.Maggs,andD.Hsu,eds.),

(Taipei,Taiwan),pp.4955,Deember1997.

[17℄ S.Q.Zheng,K.Li,Y.Pan,and M.C.Pinotti, Newaddressingshemesforpipelinedoptialbuses,in6th International

ConfereneonParallelInteronnets(PI'9)(M.Haney,R.Kostuk,C.Lund,andE.Sheneld,eds.),(Anhorage,AK,

USA),pp.230237,Otober1999.

[18℄ Z.Guo,Sortingonarrayproessorswithpipelinedbuses,inProeedingsofthe1992InternationalConfereneonParallel

Proessing,pp.280292,1992. Vol.3.

[19℄ Z.Guo,R.Melhem,R.Hall,D.Chiarulli,andS.Levitan,Pipelinedommuniationsonoptialbusses,inProeedingsof

SpietheInternationalSoietyforOptialEngineering,(Boston,MA,USA),pp.415426,Nov1990.

[20℄ Z.Guo andR.G.Melhem,Embeddingpyramidsinarrayproessors withpipelined busses,inProeedingsof the

Inter-national Conferene onAppliation Spei Array Proessors (Cat.No.90CH2920-7) (S.-Y.Kung,E. Swartzlander,

J.Fortes,andK.Przytula,eds.),(Prineton,NJ,USA),pp.665676,September1990.

[21℄ G.Ziheng,R.Melhem,R.Hall,D.Chiarulli, andS.Levitan,Pipelined ommuniationson optialbusses, inPro.of

Spie,pp.41526,1991.

[22℄ Z.Guo,R.G.Melhem,R.W.hall,D.M.Chiarulli,andS.P.Levitan,Pipelinedommuniationsinoptiallyinteronneted

arrays,JournalofParallelandDistributedComputing,vol.12,pp.269282,1991.

[23℄ Z.Guo,Optiallyinteronnetedproessorarrayswithswithingapability,JournalofParallelandDistributedComputing,

vol.23,pp.314329,Deember1994.

[24℄ G.Ziheng,Optiallyinteronneted proessor arrayswithswithingapability, Journal ofParallel &Distributed

Com-puting,vol.23,pp.31429,De.1994.

[25℄ S.PavelandS.G.Akl,Onthepowerofarrayswithoptialpipelinedbuses,inPro.oftheInternational Confereneon

Parallel andDistributedProessingTehniquesandAppliations(PDPTA'96),Vol.III(H.Arabnia,ed.),(Sunnyvale,

California,USA),pp.14431453,August1996.

[26℄ M.Hamdi,C.Qiao,andY.Pan,Onthe omputingpower ofarraysofproessorswithoptialpipelinedbuses, Parallel

Proessing Letters,vol.8,pp.503513,De.1998.

[27℄ M.MiddendoftandH.ElGindy,Matrixmultipliationonproessorarrayswithoptialbuses,Informatia,vol.22,pp.255

62,Ot.1998.

[28℄ A.BourgeoisandJ.Trahan,Relatingtwo-dimensionalreongurablemesheswithoptiallypipelinedbuses,inProeedings

14thInternationalParallelandDistributedProessingSymposium(IPDPS2000),(LosAlamitos,CA,USA),pp.747

52,May2000.

[29℄ A.BourgeoisandJ.Trahan,Relatingtwo-dimensionalreongurablemesheswithoptiallypipelinedbuses,International

JournalofFoundationsofComputerSiene,vol.11,pp.55371,De.2000.

[30℄ Y.Li,J.Tao,andS.Zheng,Asymmetriproessorarraywithsynhronousoptialbusesandswithes,ParallelProessing

Letters,vol.8,no.3,pp.283295,1998.

[31℄ Y. Pan, Order statistis on a linear array witha reongurable bus, Future Generation Computer Systems, vol. 11,

pp.321328,June1995.

[32℄ Y.Pan,Basidata movementoperationsontheLARPBS model,inParallel ComputingUsingOptialInteronnetions

(K.Li,Y.Pan,andS.-Q.Zheng,eds.),pp.227247,KluwerAademiPublishers,1998.

[33℄ J.L.Trahan, A. G.Bourgeois, Y.Pan, and R.Vaidyanathan, Optimallysaling permutationrouting onreongurable

lineararrays withoptial buses, Journal of Parallel and Distributed Computing, vol.60,pp.11251136, September

2000.

[34℄ J.L.Trahan, A. G.Bourgeois, Y.Pan, and R.Vaidyanathan, Optimallysaling permutationrouting onreongurable

lineararrays withoptialbuses, inSeond Merged Symposium IPPS/SPDP, 13thInternational Parallel Proessing

Symposium&10thSymposiumonParallelandDistributedProessing,(SanJuan,PuertoRoo),April1999.

[35℄ M.Hamdi,Enhanedmesh-onnetedomputersforimageproessingappliations,inProeedings.CAMP'95Computer

ArhiteturesforMahinePereption(Cat.No.95TB8093).IEEEComput.So.Press.1995(V.Cantoni,L.Lombardi,

M.Mosoni,M.Savini,andA.Setti,eds.),(Como,Italy),pp.375383,Sept1995.

[36℄ C.Qiao, Ondesigning ommuniation-intensivealgorithmsfor a spanningoptial bus based array, Parallel Proessing

So.Press.1996,(Tokyo,Japan),pp.183188,June1996.

[38℄ M. Hamdiand Y. Pan, Communiation-eient algorithmson reongurable arrayof proessors withspanning optial

buses,inProeedings.SeondInternationalSymposiumonParallelArhitetures,Algorithms,andNetworks(I-SPAN

'96) (Cat.No.96TB100044). IEEEComput. So.Press.1996 (G.-J.Li,D. Hsu,S.Horiguhi, andB.Maggs, eds.),

(Beijing,China),pp.440446,June1996.

[39℄ Y.MeiandChunming-Qiao,Embeddingbinarytreesinarrayswithoptialbusses,inProeedingsoftheFourth

Interna-tionalConfereneonMassivelyParallelProessingUsingOptialInteronnetions(J.Goodman,S.Hinton,T.Pinkston,

andE.Shenfeld,eds.),(Montreal,Canada),June1997.

[40℄ C.Qiao,Aunique designofber-opti interonnetion networksand algorithms, inParallel Computing UsingOptial

Interonnetions(K.Li,Y.Pan,andS.-Q.Zheng,eds.),pp.163184,KluwerAademiPublishers,1998.

[41℄ C.QiaoandY.Mei,Animprovedembeddingofbinarytreesinasquarereongurablearraywithspanningoptialbuses,

ParallelProessingLetters,vol.8,no.3,pp.321336,1998.

[42℄ M.Hamdi,C.Qiao,Y.Pan,andJ.Tong,Communiation-eientsortingalgorithmsonreongurablearrayofproessors

withslottedoptialbuses,JournalofParallelandDistributedComputing,vol.57,pp.166187,May1999.

[43℄ Y.MeiandC.Qiao,Aneientembeddingofbinarytreesinreongurablearrayswithspanningoptialbuses,

Interna-tionalJournal ofDistributedSystems&Networks,vol.2,no.1,pp.4048,1999.

[44℄ S.PavelandS.Akl,Integersortingandroutinginarrayswithreongurableoptialbuses,inProeedingsof 25th

Inter-nationalConfereneonParallelProessing(A.Bojanzyk,ed.),(Ithaa,NY,USA),pp.9094,Aug1996.

[45℄ S.Rajasekaran andS.Sahni, Sorting and routingon the arraywithreongurable optial buses, inPro. 1996 IEEE

2edInternationalConfereneonAlgorithmsandArhiteturesforParallelProessing(ICA3PP'96),(Singapore),June

1996.

[46℄ S.PavelandS.Akl,Integersortingandroutinginarrayswithreongurableoptialbuses,inProeedingsofthe

Interna-tionalConfereneonParallelProessing,(Bloomingdale,Illinois),pp.9094,August1996. volume2.

[47℄ S.PavelandS.Akl,Eientalgorithmsforthehoughtransformonarrayswithreongurableoptialbuses,inProeedings

oftheInternationalParallel ProessingSymposium,(Maui,Hawaii),pp.697701,April1996.

[48℄ S.PavelandS.Akl,Matrixoperationsusingarrayswithreongurableoptialbuses,Journal ofParallelAlgorithmsand

Appliations,vol.8,pp.223242,1996.

[49℄ S.Rajasekaran and S.Sahni,Deterministi routingon the array withreongurable optial buses, Parallel Proessing

Letters,,vol.7,pp.219224,Sept1997.

[50℄ S.Rajasekaran and S.Sahni,Computing on the array withreongurable optial buses, inWorldMultionferene on

Systemis,Cybernetis,andInformatis,(Caraas,Venezuela),pp.459466,1997.

[51℄ S.RajasekaranandS.Sahni,Sorting,seletion,androutingonthearraywithreongurableoptialbuses,IEEE

Trans-ationsonParallel&DistributedSystems,vol.8,pp.112332,Nov.1997.

[52℄ S.Pavel and S.Akl, Integer sortingand routing inarrays withreongurable optial buses, International Journal of

FoundationsofComputerSiene,SpeialIssueonInteronnetionNetworks,vol.9,pp.99120,Marh1998.

[53℄ S.D. Pavel and S.G. Akl, Computing the hough transform on arrays withreongurable optial busses, in Parallel

Computing Using Optial Interonnetions (K. Li, Y.Pan, and S.-Q. Zheng, eds.), pp.205226, Kluwer Aademi

Publishers,1998.

[54℄ S.RajasekaranandS.Sahni,Fundamentalalgorithmsforthearraywithreongurableoptialbusses,inParallel

Comput-ingUsingOptialInteronnetions(K.Li,Y.Pan,andS.-Q.Zheng,eds.),pp.185204,KluwerAademiPublishers,

1998.

[55℄ C.-H.Wu,S.-J.Horng, andH.-R. Tsai.,Templatemathingon arrayswithreongurable optial buses, inOperations

Researh and its Appliations. Third International Symposium (ISORA'98)(D.-Z.Du, X.-S. Zhang,and K.Cheng,

eds.),(Kunming,China),Aug.1998.

[56℄ H.ElgindyandS.Rajesekaran,Sortingandseletiononalineararraywithoptialbussystem,ParallelProessingLetterS,

vol.9,pp.373383,Sept1999.

[57℄ C.-H.Wu,S.-J.Horng,andH.-R.Tsai,Eientparallelalgorithmsforhierarhiallusteringonarrayswithreongurable

optialbuses,Journal ofParallel&DistributedComputing,vol.60,pp.113753,Sept2000.

[58℄ C.-H.Wu, S.-J.Horng,H.-R. Tsai,J.-F. Lin,and T.-L.Lin, Anoptimal parallelalgorithmfor omputingmomentson

arrayswithreongurable optialbuses, inPro. 14thInternationalParallel and DistributedProessing Symposium

(IPDPS2000),(LosAlamitos,CA,USA),pp.7416,May2000.

[59℄ C.-H.Wu,S.-J.Horng,Y.-R.Wang,andL.-G.Jeng,Parallelalgorithmsforvetormedianltering,inProeedingsofthe

4thInternationalConfereneonAlgorithmsandArhiteturesforParallelProessing,pp.24051,2000.

[60℄ C.-H.WuandS.-J.Horng,L/sub2/vetormedianltersonarrayswithreongurableoptialbuses,IEEETransations

onParallel andDistributedSystems,vol.12,no.12,pp.128192,De.2001.

[61℄ C.-H.Wuand S.-J.Horng, Salableand optimal speed-upparallelalgorithmsfortemplatemathingon arrays with

re-ongurableoptialbuses,InternationalJournal ofFoundationsofComputerSiene,vol.14,no.1,pp.7998,Feb.

2003.

[62℄ C.-H.WuandS.-J.Horng,Fastandsalableseletionalgorithmswithappliationstomedianltering,IEEETransations

onParallel andDistributedSystems,vol.14,pp.98392,Ot.2003.

[63℄ Y.PanandK.Li,Lineararraywithareongurablepipelinedbussystemoneptsandappliations, inPro.of the

International Conferene onParallel and Distributed Proessing Tehniquesand Appliations(PDPTA'96),Vol.III

(H.Arabnia,ed.),(Sunnyvale,California,USA),pp.14311441,August1996.

[64℄ R.RoldanandB.J.d'Auriol,Apreliminaryfeasibilitystudyofthe LARPBSoptialbusparallelmodel,inProeedings

of the17thInternational Symposiumon HighPerformane ComputingSystemsand Appliations(HPCS2003) and

[65℄ H. Kimm, Inversion number algorithm on a linear array with a reongurable pipelined bus system, in Pro. of the

International ConfereneonParallel andDistributed Proessing Tehniquesand Appliations(PDPTA'96),Vol.III

(H.Arabnia,ed.),(Sunnyvale,California,USA),pp.13981407,August1996.

[66℄ Y. Pan,K.Li,and S.-Q.Zheng, Fastnearest neighboralgorithmson alinear arraywithareongurable pipelined bus

system,inProeedings.ThirdInternationalSymposiumonParallelArhitetures,Algorithms,andNetworks(I-SPAN

'97)(Cat.No.97TB100209).IEEEComput.So.1997(F.Lai,B.Maggs,andD.Hsu,eds.),(Taipei,Taiwan),pp.444

450,De1997.

[67℄ B.Cong, Onembeddingsofneuralnetworksintomassivelyparallelomputersystems, inProeedingsof theIEEE1997

NationalAerospaeandEletronisConferene.NAECON1997.,(Dayton,OH),pp.231238,July1997.

[68℄ J. L. Trahan, Y. Pan, R. Vaidyanathan, and A. G. Bourgeois, Salable basi algorithms on a linear array with a

reongurablepipelinedbussystem,in10thInternationalConfereneonParallelandDistributedComputingSystems,

(NewOrleans,LA,USA),pp.564569,1997.

[69℄ H. Kimm, Parallel total weight rossing number algorithm for hannel routing on a linear array with a

reong-urable pipelined bussystem, inProeedings of theTwenty-Ninth Southeastern Symposium onSystem Theory (Cat.

No.97TB100097). IEEEComput.So.Press. 1997,(Cookeville,TN,USA),pp.183187,Marh1997.

[70℄ K.Li,Booleanmatrixmultipliationonalineararraywithareongurablepipelinedbussystem,inPro.ofthe11th

An-nualInternationalSymposiumonHighPerformaneComputingSystems(HPCS'97),(Winnipeg,Manitoba,Canada),

pp.179190,July1997.

[71℄ K.Li,Constanttimebooleanmatrixmultipliationonalineararraywithareongurablepipelinedbussystem,Journal

ofSuperomputing,vol.11,no.4,pp.391403,1997.

[72℄ K.Li,Y.Pan,andS.-Q.Zheng,Salableparallelmatrixmultipliationusingreongurablepipelinedoptialbussystems,

in Proeedings of the 10th IASTED International Conferene on Parallel and Distributed Computing and Systems

(Y.Pan,S.G.Akl,andK.Li,eds.),(LasVegas,Nevada,USA),pp.238243,Ot.1998.

[73℄ K.Li,Y.Pan,and S.-Q.Zheng, Fastand eient parallelmatrixomputationson alinear array withareongurable

pipelinedoptialbussystem,inProeedingsofHPCS'98:12thAnnualInternationalSymposiumonHighPerformane

ComputingSystems(J.Shaeer,ed.),(Calgary,Alta.,Canada),pp.363380,May1998.

[74℄ Y.Pan,M.Hamdi,andK.Li,Eientandsalablequiksortonalineararraywithareongurablepipelinedbussystem,

FutureGenerationsComputerSystems,vol.13,pp.501513,May1998.

[75℄ Y. Pan and K.Li, Linear array with a reongurable pipelined bus system.onepts and appliations., Information

Sienes,vol.106,pp.237258,May1998.

[76℄ K.Li,Fastmatrixmultipliationandrelatedoperationsusingreongurableoptialbusses,inParallelComputingUsing

OptialInteronnetions(K.Li,Y.Pan,andS.-Q.Zheng,eds.),pp.248273,KluwerAademiPublishers,1998.

[77℄ K.Li,Y.Pan,andS.Q.Zheng,Fastandproessoreientparallelmatrixmultipliationalgorithmsonalineararraywith

areongurable pipelinedbussystem, IEEETransationsonParallel and DistributedSystems, vol.9,pp.705720,

August1998.

[78℄ Y. Pan,K.Li,and S.-Q.Zheng, Fastnearest neighboralgorithmson alinear arraywithareongurable pipelined bus

system,Parallel AlgorithmsandAppliations,vol.13,pp.125,1998.

[79℄ K.Li,Y.Pan,andS.Zheng,Parallelmatrixomputationsusingareongurablepipelinedoptialbus,JournalofParallel

&DistributedComputing,vol.59,pp.1330,Ot1999.

[80℄ Y. Han, Y. Pan, and H.Shen, Fast parallelseletion on the linear arraywith reongurable pipelined bus system, in

Proeedings. Frontiers'99.Seventh Symposium onthe Frontiersof MassivelyParallel Computation.IEEE Comput.

So.1999,(Annapolis,MD,USA),pp.286293,Feb1999.

[81℄ K.LiandV.Pan,Parallelmatrixmultipliationonalineararraywithareongurablepipelinedbussystem,in

Proeed-ings 13thInternational Parallel Proessing Symposium and10th Symposium onParallel and Distributed Proessing.

IPPS/SPDP1999,(SanJuan,PuertoRio),pp.3135,April1999.

[82℄ K.Li, Y.Pan, and M.Hamdi, Solvinggraphtheory problems usingreongurable pipelined optial buses, inParallel

and DistributedProessing. 11thIPPS/SPDP'99 Workshopsheldin onjuntionwiththe13thInternational Parallel

Proessing Symposium and the 10th Symposium on Parallel and Distributed Proessing, (San Juan, Puerto Rio),

pp.911923,April1999.

[83℄ K.Li,Y.Pan,andS.Zheng,EientdeterministiandprobabilistisimulationsofPRAMsonlineararrayswith

reong-urablepipelinedbussystems,JournalofSuperomputing,vol.15,pp.163181,Feb2000.

[84℄ B.J.d'Auriol,CommuniationintheLARPBS(optialbus)model: Aasestudy, inPro.ofTheFourthInternational

ConfereneonAlgorithms AndArhitetureforParallel Proessing (ICA3PP2000)(A.G.etal.,ed.),(HongKong),

pp.581590,Deember2000.

[85℄ A.DattaandS.Soundaralakshmi,Computingonnetedomponentsonalineararraywithareongurablepipelinedbus

system,inProeedingsofPART2000.SeventhAustralasianConfereneonParallelandReal-TimeSystems(H.ElGindy

andC.Fidge,eds.),(Sydney,NSW,Australia),pp.181191,Nov2000.

[86℄ K. Li, Y. Pan, and M. Hamdi, Solving graph theory problems using reongurable pipelined optial buses, Parallel

Computing,vol.26,pp.723735,May2000.

[87℄ M.HeandS.Q.Zheng,Anoptimalsortingalgorithmonalineararraywithreongurablepipelinedbussystem,inPDCS

2002: 15thInternationalConfereneonParallelandDistributedComputingSystems,pp.38691,2002.

[88℄ A. Datta and Soundaralakshmi, Fast and salable algorithms for the eulidean distane transform on the larpbs, in

Proeedings of IPDPS Workshop on Advanes in Parallel and Distributed Computational Models, (San Franiso),

April2001.

[89℄ K.LiandV.Y.Pan,Parallelmatrixmultipliationonalineararraywitha reongurablepipelinedbussystem, IEEE

TransationsonComputers,vol.50,pp.519525,May2001.

[90℄ A.Datta,Eientgraphalgorithmsonalineararraywithareongurablepipelinedbussystem,inProeedingsofIEEE

[92℄ Y.Pan,Y. Li,J.Li, K.Li,and S.Zheng, Eientparallelalgorithms fordistane mapsof2d binary imagesusingan

optialbus, IEEETransationsonSystems,Man,andCybernetis-PartA:SystemsandHumans,vol.32,pp.228

236,Marh2002.

[93℄ Y.Pan,Y. Li,J.Li, K.Li,and S.Zheng, Eientparallelalgorithms fordistane mapsof2d binary imagesusingan

optialbus, IEEETransationsonSystems,Man,andCybernetis-PartA:SystemsandHumans,vol.32,pp.228

236,Marh2002.

[94℄ A.Datta, Eientgraph-theoreti algorithmson a lineararraywitha reongurable pipelinedbus system, Journal of

Superomputing,vol.23,pp.193211,Sept2002.

[95℄ A.Datta,S.Soundaralakshmi,andR.Owens,Fastsortingalgorithmsonalineararraywithareongurablepipelinedbus

system,IEEETransationsonParallel andDistributedSystems,vol.13,pp.212222,Marh2002.

[96℄ Y.Han,Y.Pan,and H.Shen,Sublogarithmideterministiseletiononarrayswithareongurableoptial bus, IEEE

TransationsonComputing,vol.51,pp.702707,June2002.

[97℄ J.Li,Y.Pan,andH.Shen,Moreeienttopologialsortusingreongurableoptialbuses,TheJournal of

Superom-puting,vol.24,pp.251258,Marh2003.

[98℄ H.KimmandD.Semé,Longestrepeatedsuxproblemonthearrayswithpipelinedoptialbussystems,inProeedings

ofthe35thSoutheasternSymposiumonSystemTheory,(Morgantown,WV,USA),pp.6973,Marh2003.

[99℄ Y.Pan,ComputingontherestritedLARPBSmodel,inPro.ofThe2003InternationalSymposiumonParalleland

Dis-tributedProessingandAppliations,(Aizu-WakamatsuCity,Japan),pp.913,July2003.Leture NotesinComputer

Siene,vol.2745.

[100℄ A.G.BourgeoisandJ.L.Trahan,Faulttolerantalgorithmsforalineararraywithareongurablepipelinedbussystem,

ParallelAlgorithmsandAppliations,vol.18,pp.139153,September2003.

[101℄ L.Chen, Y.Pan,andX.Xu,Salable andeientparallelalgorithmsforeulideandistanetransformon theLARPBS

model,IEEETransationsonParallelandDistributedSystems,toappear,2004.

[102℄ L.Chen,H.Chen,Y.Pan,andY.Chen,AfasteientparallelhoughtransformalgorithmonLARPBS, TheJournalof

Superomputing,vol.29,pp.185195,2004.

[103℄ B.J.d'AuriolandR.Molakaseema,Aparameterizedlineararraywithareongurablepipelinedbussystem:LARPBS(p)),

TheComputerJournal,vol.48,no.1,pp.115125,2005.

[104℄ A.DattaandS.Soundaralakshmi,Fastandsalablealgorithmsfortheeulideandistanetransformonalineararraywitha

reongurablepipelinedbussystem,JournalofParallelandDistributedComputing,vol.64,no.3,pp.360369,2004.

[105℄ Y.Li,Y.Pan,andS.Zheng,Pipelinedtime-divisionmultiplexingoptialbuswithonditionaldelays,OptialEngineering,

vol.36,pp.24172424,September1997.

[106℄ J.Fernandez-Zepeda,R.Vaidyanathan,andJ.Trahan,Improvedsalingsimulationofthegeneralreongurablemesh,in

Proeedings.ParallelandDistributedProessing,11IPPS/SPDP'99Workshops,(SanJuan,PuertoRio),pp.615624,

April1999.

[107℄ J.Fernandez-Zapeda,R.Vaidyanathan,andJ.Trahan,Usingbuslinearizationtosalethereongurablemesh, Journal

ofParallelandDistributedComputing,vol.62,pp.495516,April2002.

[108℄ B.J.d'AuriolandM.Beltran,Optialbusommuniationmodelingandsimulation,inPro. oftheInternational

Sym-posiumonHighPerformaneComputingSystemsandAppliations(HPCS2004)(M.R.Eskiioglu,ed.),(Winnipeg,

Manitoba,Canada),pp.135142,May2004.

Editedby: MarinPapzyki

Reeived: November27,2003