Swarm Intelligence for Routing in Communication Networks

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1 Swam Itellgece fo Routg Commucato Netwo I. Kaabal *,M.A.El-Shaaw *, R.J.Ma II *, P. Aabhah,A.A.Gay, _ * ept. of Electcal Eg., Box Uvety of Wahgto Seattle, WA 9895 USA [a,melha,ma]@ee.wahgto.eu Jet Populo Laboatoy 4800 Oa Gove ve, MS Paaea, CA 909 USA [payma,gay]@jpl.aa.gov Abtact Swam tellgece, a emotate by atual bologcal wam, ha umeou poweful popete eable may egeeg ytem, uch a etwo outg. I ato, ew paagm fo egg autoomou a calable ytem may eult fom aalytcally uetag a exteg the eg pcple a opeato exhbte by tellget bologcal wam. A ey elemet of futue eg paagm wll be emeget tellgece mple local teacto of autoomou wam membe, wth mple pmtve, gvg e to complex a tellget global behavo. Commucato etwo maagemet becomg ceagly fcult ue to the ceag ze, aply chagg topology, a complexty of commucato etwo. A ew cla of algothm, pe by wam tellgece, cuetly beg evelope that ca potetally olve umeou poblem of moe commucato etwo. Thee algothm ely o the teacto of a multtue of multaeouly teactg aget. A uvey of uch algothm a the pefomace peete hee. I. INTROUCTION Moe commucato etwo ae becomg ceagly vee a heteogeeou. Th the coequece of the ato of a ceag aay of evce a evce, both we a wele. The ee fo eamle teacto of umeou heteogeeou etwo compoet epeet a fomable challege, epecally fo etwo that have tatoally ue cetalze metho of etwo cotol. Th tue fo both pacet-wtche a vtualccut etwo, a the Iteet, whch becomg a eve moe complex collecto of a vety of ubet. The ee to copoate wele a pobly a-hoc etwo to the extg we-l fatuctue ee the equemet fo effcet etwo outg eve moe emag. Routg algothm moe etwo mut ae umeou poblem. Two of the uual pefomace metc of a etwo ae aveage thoughput a elay. The teacto betwee outg a flow cotol affect how well thee metc ae jotly optmze. Betea a Gallage [] ote that the balace of elay a thoughput eteme by the flow-cotol cheme goo outg eult a moe favoable elay-thoughput cuve. Qualty of evce (QoS) guaatee aothe mpotat pefomace meaue [2,3]. Hee, a ue mght eque a guaatee allocato of bawth, a maxmum elay, o a mmum hop-cout. Such guaatee oly mae ee fo vtual-ccut etwo [2]. Th becaue applcato that eque logcal coecto thee ema fo a mmum flow ate of ata. Th ule pacet-wtche type of evce whee bet-effot outg mplemete. Although logcal coecto ue tatc outg, the etablhmet of the coecto poe to the ame poblem that affect outg the et of the etwo [3]. Cuet outg algothm ae ot aequate to tacle the ceag complexty of uch etwo. Cetalze algothm have calablty poblem; tatc algothm have touble eepg up-to-ate wth etwo chage; a othe tbute a yamc algothm have ocllato a tablty poblem []. Swam tellgece outg pove a pomg alteatve to thee appoache. Swam tellgece utlze moble oftwae aget fo etwo maagemet. Thee aget ae autoomou ette, both poactve a eactve, a have the capablty to aapt, coopeate a move tellgetly fom oe locato to the othe the commucato etwo [4]. Swam tellgece, patcula, ue tgmegy (.e. commucato though the evomet) fo aget teacto [5,6,7,9]. Swam tellgece exhbt emeget behavo whee mple teacto of autoomou aget, wth mple pmtve, gve e to a complex behavo that ha ot bee pecfe explctly [8]. I Secto II, we gve a ovevew of extg outg algothm, clug the vual met a weaee. A cuo of wam tellgece a t attactve featue appea Secto III a, Secto IV, we peet ome pecfc wam-bae algothm a cu the applcablty a pefomace. Secto V coclue the pape. II. ROUTING ALGORITHMS Routg algothm ca be clafe a tatc o yamc, a cetalze o tbute. Cetalze algothm ae uually ue legacy outg ytem a have poblem wth calablty a oate ema fo maagg eco equg huma atteto [0]. Aothe awbac the ablty of the etwo to ecove cae of falue at the cetal cotollg tato. Statc outg aume that etwo coto ae tme-vaat. The metho oe ot ae the etwo loa whe tyg to f the hotet-path oute. Ahuja, Magat, a Ol [] how that maxmzg thoughput fo a tme vayg loa a lmte-capacty tamo le a NP-complete poblem. Aaptve outg cheme alo have poblem, clug cotece ag fom oe falue a potetal ocllato that lea to ccula path a tablty []. Aothe poblem wth aaptve algothm apple to a-hoc etwo ae whe chage the etwo occu too fequetly to allow outg upate to popagate thoughout all etwo oe. A etwo calle combatoally table f t chage uffcetly lowly fo the outg upate to be popagate to all the oe [3]. Routg algothm ca alo be clafe a mmal o o-mmal. Mmal outg allow pacet to follow oly mmal cot path, whle o-mmal outg allow moe flexblty choog the path by utlzg othe heutc [2]. Mmal outg ca futhe be ubve to optmal outg a hotet-path outg. Ithefome,theobjectve to optmze the mea flow of the ete etwo; whle hotet-path outg the goal to f the mmum-cot path betwee two oe [,7]. Aothe cla of outg algothm oe whee the outg cheme guaatee pecfe QoS equemet petag to elay a bawth. Thee algothm ae uually meage bae,.e. they f a feable path atfyg the QoS cotat bae o a exchage of meage betwee the oe []. Thee algothm have the teecy to tempoaly oveue etwo eouce utl they f the

2 appopate path. The jta a Bellma-Fo algothm [] ae example. Yet aothe fom of etwo cotol, whch ele heavly o outg, that of loa balacg [7,9,9,20]. Hee the goal to balace the loa thoughout all etwo eouce wthout lee a oveloag. III. SWARM INTELLIGENCE OVERVIEW Swam Itellgece appea bologcal wam of ceta ect pece. It gve e to complex a ofte tellget behavo though complex teacto of thoua of autoomou wam membe. Iteacto bae o pmtve tct wth o upevo. The e eult accomplhmet of vey complex fom of ocal behavo a fulfllmet of a umbe of optmzato a othe ta [6]. The ma pcple beh thee teacto calle tgmegy, o commucato though the evomet. A example pheomoe layg o tal followe by at. Pheomoe a potet fom of homoe that ca be ee by at a they tavel alog tal. It attact at a theefoe at te to follow tal that have hgh pheomoe cocetato. Th caue a autocatalytc eacto,.e., oe that acceleate by telf. At attacte by the pheomoe wll lay moe of the ame o the ame tal, caug eve moe at to be attacte. Aothe fom of tgmegy alte the evomet uch a mae a to pomote futhe mla acto by the aget. Th poce ubbe ta-elate tgmegy. A example agalaygbytemtewhecotuctget[6].i the tal tage of cotucto, temte lay a ga at aom locato. Th tmulate futhe layg by othe membe of the wam, utl a gle heap of a ga aomly eache a ctcal ma that lage tha t eghbog heap. At that pot, mot temte ae attacte to that pecfc heap, theeby electg that pecfc te fo cotucto of the et. Swam tellgece boat a umbe of avatage ue to the ue of moble aget a tgmegy [2,3,4,6,7,8,9]. Thee ae:. Scalablty: Populato of the aget ca be aapte accog to the etwo ze. Scalablty alo pomote by local a tbute aget teacto. 2. Fault toleace: Swam tellget pocee o ot ely o a cetalze cotol mecham. Theefoe the lo of a few oe o l oe ot eult catatophc falue, but athe lea to gaceful, calable egaato. 3. Aaptato: Aget ca chage, e o epouce, accog to etwo chage. 4. Spee: Chage the etwo ca be popagate vey fat, cotat wth the Bellma-Fo algothm []. 5. Moulaty: Aget act epeetly of othe etwo laye [9]. 6. Autoomy: Lttle o o huma upevo eque. 7. Paallelm: Aget opeato ae heetly paallel. Thee popete mae wam tellgece vey attactve fo a-hoc wele etwo. They alo ee wam tellgece utable fo a vaety of othe applcato, apat fom outg, clug obotc [2,3,4] a optmzato [5,6,7]. IV. SWARM INTELLIGENCE ROUTING: EXAMPLES Thee ae a umbe of popoe wam-bae outg algothm. The mot celebate oe AtNet [6,7], a aaptve aget-bae outg algothm that ha outpefome the bet-ow outg algothm o eveal pacet-wtche commucato etwo. Fo telephoe etwo, thee alo ext a ucceful applcato of wam tellgece ubbe At-Bae Cotol (ABC) [6,9,20]. Heue et al. [8] gve aothe teetg example ug a vaato of wam outg bae o Bellma' pcple of yamc pogammg [2]. Thee algothm ae cue futhe etal below. Othe example alo ext a peet ome teetg vaato of wam-bae outg. Oa & Maatoh [2] peet a algothm ubbe aget-bae outg ytem (ARS) whoe ma goal to acheve hgh utlzato of etwo eouce. The autho popoe a exteo of the AtNet algothm wth QoS guaatee, mpog ceta etcto o bawth a hop-cout. Lppet & Kelle [9], tae a feet aget bae appoach fo loa balacg. They popoe the ue of two clae of aget, ubbe tategy aget a loa aget. The ole of the loa aget to f hotet path bae o jta algothm [22]. The tategy aget cotol the populato of the loa aget bae o etwo coto. Vaella & Scla [23] apply wam tellgece fo vtual-wavelegth-path outg. They popoe the epaato of at to coloe, wth at beg attacte to the pheomoe of the ow coloy a epelle by pheomoe of othe coloe. Thu, at of each coloy attempt to cove the hotet path epeet fom the path covee by othe coloe. Th lea to a moe eve loa tbuto thoughout the etwo. Moe example of wam bae outg applcato ext the lteatue. Boabeau et al. [24] cu a mpovemet of at-bae algothm by yamc pogammg. Cao a ogo [25-30] peet a umbe of teetg vaato bae o at-le aget. Whte et al. alo cu vaou ehacemet of outg algothm [3-35]. A. AtNet I the AtNet algothm, outg eteme by mea of vey complex teacto of fowa a bacwa etwo exploato aget ( at ). The ea beh th ubvo of aget to allow the bacwa at to utlze the ueful fomato gathee by the fowa at o the tp fom ouce to etato. Bae o th pcple, o oe outg upate ae pefome by the fowa at. The oly pupoe lfe to epot etwo elay coto to the bacwa at, the fom of tp tme betwee each etwo oe. The bacwa at het th aw ata a ue t to upate the outg table of the oe. A example of a AtNet outg table Table I. The ete of the outg table ae pobablte, a a uch, mut um to fo each ow of the etwo. Thee pobablte eve a ual pupoe: () the exploato aget of the etwo ue them to ece the ext hop to a etato, aomly electg amog all caate bae o the outg table pobablte fo a pecfc etato (2) the ata pacet etemtcally elect the path wth the hghet pobablty fo the ext hop. TABLE I. ANTNET ROUTING TABLE etato Next Hop E F The equece of acto AtNet (ee Fg. ) mple a tutve:. Each etwo oe lauche fowa at to all etato egula tme teval. 2. The at f a path to the etato aomly bae o the cuet outg table.

3 3. The fowa at ceate a tac, puhg tp tme fo evey oe a that oe eache 4. Whe the etato eache, the bacwa at het the tac. 5. The bacwa at pop the tac ete a follow the path evee. 6. The oe table of each vte oe ae upate bae o the tp tme. (a) AB 0.23 A B C BC 0. E C 0.4 BC 0. F (b) AB 0.23 A B C BC 0. E C 0.4 BC 0. Fg.. (a) Fowa at movemet (b) Bacwa at movemet The upate of the outg table emcet of othe acto-ctc ytem, whee the aw fomato cotae the tp tme pocee by the ctc a the ue to ta the acto to maage the ytem moe effcetly (ee Fg. 2). Raw Refocemet Ctc Pocee Refocemet Fg. 2. Acto-Ctc Sytem Leag Sytem F Acto A a temeate quatty the poceg of the aw tp tme fomato, we ee a meaue that tae o mall value whe the tp tme hot elatve to the mea a vce-vea. Th quatty, ', eve accog to: T T, c, f < ' = c c, othewe whee T the tp tme, aveage of T, ac a calg facto, uually et to 2. Except fo the outg table, each oe alo poee a table wth eco of the mea a vaace of the tp tme to evey etato. A typcal tp-tme table Table II. TABLE II. ANTNET ROUTING TABLE etato Tp Tme E F The ato of the vaace to the mea, ( σ ), ue a a meaue of the cotecy of the tp tme, a to accogly alte the effect of the tp tme o the outg table. Bae o the value of, we eteme the elatve gooe of the tp tme of a at. Coepog tatege of ethe eceag o ceag the value of by a ceta amout ae the followe, bae o ettg the thehol fo the goo/ba tp tme to 0.5, a electg a thehol δ fo the ( σ ) ato (ee Table III). σ >δ σ <δ TABLE III. PROCESSING CASES <0.5 >0.5 ' σ ' σ + ( e ) ( e ) σ e σ + e The pcple beh thee upate that mall value of coepo to mall value of T a vce vea. By way of example, a examg the cae whee the cotecy hgh a the tme goo, we wat the pocee to be eve malle. og o uecoe the gooe of th tp tme a t cotecy. Theefoe, a expoetal quatty ubtacte. Th quatty the expoetally ecayg fucto of the cotecy ato a acheve t hghet value whe the vaace vey mall. The ecay ate ca be cotolle though paamete a a a. Futhe potve o egatve efocemet of goo o ba oute tae place ext, va egatve feebac. Ay potve efocemet of pobablty houl be egatvely popotoal to cuet pobablte, a ay egatve efocemet houl be popotoal to cuet pobablte. The effect of th to pevet atuato to 0 o of the outg table pobablte. The oe that eceve the potve efocemet the oe fom whch the bacwa at come. Th the ame oe choe by the fowa at a ext-hop o the way to t etato. All the othe eghbo of the cuet oe ee to be egatvely efoce to peeve the ut um of all the ext-hop pobablte. The efocemet equato ae: + = ( ' )( P ) = ( ' ) P, f, N whee P, P ae the pevou outg table pobabltef the oe fom whch the bacwa at come, N the eghbohoo of oe (cuet oe), a the etato oe (ee Fg. 3). The lat tep to upate the outg table pobablte ug the followg ule. Cuet P P = P + + = P + f Neghbohoo Fg. 3. Cuet Noe Neghbohoo The pacet of the etwo the ue thee pobablte a etemtc way, choog a ext hop the oe wth the hghet pobablty. B. At-bae Cotol At-bae Cotol (ABC) aothe ucceful wam tellgece bae algothm ege fo telephoe etwo.

4 Th algothm hae may ey featue wth AtNet, but ha mpotat feece. The bac pcple hae the ue of a multtue of aget teactg ug tgmegy. The algothm aaptve a exhbt obute ue vaou etwo coto. It alo copoate aome the moto of at. Th ceae the chace of covey of ew oute. I ABC, the at oly tavee the etwo oe pobabltcally, whle the telephoe taffc follow the path of hghet pobablty. The outg table of evey oe the ame a AtNet. The upate phloophy of the outg table lghtly feet though. Thee oly oe cla of at, whch lauche fom the ouce to vaou etato at egula tme teval. The at ae elmate oce they each the etato. Theefoe, the pobablte of the outg table ae upate a the at vt the oe, bae o the lfe of the at at the tme of the vt. The lfe of the at the um of the elay of the oe T =.Theelay ae gve by c e S =,wheec, ae eg paamete a S the pae capacty of each oe the telephoe etwo. The a a tep ze efe fo that oe, accog to: δ = + b, T whee a a b ae both eg paamete. Th tep ze ule choe heutcally. It ag a geate tep ze to thoe at who ae ucceful at eachg the oe fate. The outg table the upate accog to: t, ( ) + δ, ( t + ) = + δ,, ( t + ) =, + δ efe a the um of all the cot fom oe to etato oe. Oce the etato eache, the a bacwa at lauche, whch upate the tace etmato j, fo oe to va j a follow: t j, = ( η ) j, ( ) + η, whee η the leag ate. The outg table pobablte, whoe ue mla to thoe AtNet, ae upate a follow:. whee β a o-leaty facto. β j t p j t, ( ), ( ) =, j l β, l l, The teetg mpovemet to th algothm bae o Bellma pcple of yamc pogammg. Evey oe the path J of a ouce-etato pa -, coee a etato. The bac-popagatg aget wll upate the outg table of a vte oe ot jut fo the etato, but alo fo the temeate oe. Hece the upate occu all at oce. Fo example, o oe Fg. 4, the bacwa aget wll alo upate the ety fo oe a follow: = ( η ) ( t ) + η,,, whee theouceoe, the cuet oe a - the pevou oe. etato TABLE IV. ABC ROUTING TABLE Next Hop E F Note that the at both ue a upate the outg table at the ame tme. Fo example, Table IV, f the ouce oe F a the etato oe E, the the at wll upate the ow fo F a ue the oe fo E to f the ext hop. It fucto a a at that both a fowa a a bacwa at. The upate ule ae uch that the coto, =,whee ae all the eghbo to, atfe. C. Multple Rou Tp Routg Aothe teetg example of wam tellgece apple to pacet-wtche etwo Multple Rou Tp outg [7]. A AtNet, oe lauch fowa at egula teval. The bac veo utlze the cot meaue by the fowa at to upate the outg table ete. The fowa at eep tac of the vte ote a tac J a of the aocate cot,. Th cot ca be the wat tme a the tamo elay fo each vte oe. The cot, Fg. 4. Multple Tp Routg Example AtNet a Multple Tp Routg ae two example of the cla of wam tellgece algothm that copoate ou-tp aget. I th type of algothm, the fowa at act a vetgato a the bacwa at ae the oe who upate the outg table. ABC a algothm that copoate oly fowa aget, who pefom the upate a they tavel though the etwo. I th type of algothm upate fate a moe elable, ce thee o elay betwee the fomato gatheg a the actual upate [8]. V. CONCLUSIONS I th pape, we have peete a ovevew of wam tellgece apple to etwo outg. Iheet popete of wam tellgece a obeve atue clue: mave ytem calablty, emeget behavo a tellgece fom low complexty local teacto, autoomy, a tgmegy, o commucato though the evomet. Thee popete ae eable fo may type of etwo. Swam tellget-

5 bae appoache hol geat pome fo olvg umeou poblem of a-hoc powe awae etwo. Swam tellgece howeve a ew fel a much wo ema to be oe. Compao of the pefomace of wam-bae algothm ha bee oe by emulato. Aalytc poof a moel of the wam-bae algothm pefomace ema topc of ogog eeach. REFERENCES.. Betea a R. Gallage. ata Netwo. Petce-Hall, Ic, Uppe Sale Rve, New Jeey, K. Oa a M. Seo, "A aget-bae outg ytem fo QoS guaatee", Poc. IEEE Iteatoal Cofeece o Sytem, Ma, a Cybeetc, Oct. 2-5, pp , Satyabata Chaabat a Amtabh Mha, QoS Iue A Hoc Wele Netwo, IEEE Commucato Magaze, Febuay A. Bezcza, B. Pague, a T. Whte, "Moble aget fo etwo maagemet", IEEE Commucato Suvey, Fouth Quate 998, vol., o., Gaé, P.P La ecotucto u et le cooato tevuelle chez Bellcoteme atale et Cubteme p. La theoe e la tgmege: Ea 'tepetato e temte cotucteu. I. Soc., 6, E. Boabeau, M. ogo, a G. Théaulaz, Swam tellgece: fom atual to atfcal ytem, Oxfo Uvety Pe, G. Cao a M. ogo, "AtNet: a moble aget appoach to aaptve outg", Tech. Rep. IRIIA/97-2, Uveté Lbe e Buxelle, Belgum 8. M. Heue,. Sye, S. Gué, a P. Kutz, "Aaptve aget-ve outg a loa balacg commucato etwo", Poc. ANTS'98, Ft Iteatoal Wohop o At Coloy Optmzato, Buel, Belgum, Octobe 5-6, S. Lppet a B. Kelle, "Moble aget telecommucato etwo - a mulatve appoach to loa balacg", Poc. 5th Itl. Cof. Ifomato Sytem, Aaly a Sythe, ISAS'99, Rama, L.: OSI ytem a Netwo Maagemet, IEEE Commucato: Maagemet of Heteogeeou Netwo, vol. 36, o.3, Mach 998. R. K. Ahuja, Magat T.L., a J.B. Ol. Netwo Flow: Theoy, Algothm a Applcato. Petce Hall, Ic., Uppe Sale Rve, New Jeey, Sugawaa, K.; Sao, M.; Yohhaa, I.; Abe, K.; Wataabe, Foagg behavou of mult-obot ytem a emegece of wam tellgece, Sytem, Ma, a Cybeetc, 999. IEEE SMC '99 Cofeece Poceeg. 999 IEEE Iteatoal Cofeece o, Volume: 3, 999 Page(): vol.3 3. Fuua, T.; Fuato,.; Seyama, K.; Aa, F.,Evaluato o flexblty of wam tellgetytem Robotc a Automato, 998. Poceeg. 998 IEEE Iteatoal Cofeece o, Volume:4,998 Page(): vol.4 4. Kawabata, K.; Suzu, T.; Hayama, T.; Kobayah, H., tbute tellget cotol tuctue fo mult-legge walg obot Avace Moto Cotol, 996. AMC '96-MIE. Poceeg., 996 4th Iteatoal Wohop o, Volume:,996, Page(): vol. 5. A. Colo, M. ogo, a V. Maezzo, "A vetgato of ome popete of a at algothm", Poc. Paallel Poblem Solvg fom Natue Cofeece (PPSN 92), Buel, Belgum, pp , M. ogo, V. Maezzo, a A. Colo, "The at ytem: optmzato by a coloy of coopeatg aget", IEEE Taacto o Sytem, Ma, a Cybeetc, Pat B, vol. 26, o., pp. 29-4, A. Colo, M. ogo, a V. Maezzo, "A vetgato of ome popete of a at algothm", Poc. Paallel Poblem Solvg fom Natue Cofeece (PPSN 92), Buel, Belgum, pp , S. Che a K. Nahteh, A Ovevew of Qualty-of-Seve outg fo the ext Geeato Hgh-Spee etwo IEEE Netwo, pp64-79, Nov/ec R. Schooewoe, O.E. Holla, J. Bute, L. Rothatz, "At-bae loa balacg telecommucato etwo", HP Lab Techcal Repot, HPL-96-76, May 2, R. Schooewoe, O.E. Holla, J.L. Bute, "At-le aget fo loa balacg telecommucato etwo", Poc. Ft ACM Iteatoal Cofeece o Autoomou Aget. 2. Bellma, Rcha Eet, "yamc pogammg", PcetoUvety Pe, jta, E.W.: A Note o Two Poblem Coecto wth Gaph. I: Numec Mathematc, p , G. Navao Vaela a M.C. Scla, "At coloy optmato fo vtual-wavelegth-path outg a wavelegth allocato", Poc. 999 Coge o Evolutoay Computato, Wahgto C, USA, pp , July E. Boabeau, F. Heaux, S. Gue,. Sye, P. Kutz, a G. Theaulaz, "Routg telecommucato etwo wth "mat" atle aget", Poc. Itellget Aget fo Telecommucato Applcato ' G. Cao a M. ogo, "A aaptve mult-aget outg algothm pe by at behavo", Poc. PART98 - Ffth Aual Autalaa Cofeece o Paallel a Real-Tme Sytem, Aelae, Autala, Septembe 28-29, G. Cao a M. ogo, "At coloe fo aaptve outg pacetwtche commucato etwo", Poc. PPSN V - Ffth Iteatoal Cofeece o Paallel Poblem Solvg fom Natue, Amteam, Holla, Septembe 27-30, G. Cao a M. ogo, "Exteg AtNet fo bet effot qualty-ofevce outg", Poc. ANTS'98 - Ft Iteatoal Wohop o At Coloy Optmzato, Buel, Belgum, Octobe 5-6, G. Cao a M. ogo, "Two at coloy algothm fo bet-effot outg atagam etwo", Poc. 0th Iteatoal Cofeece o Paallel a tbute Computg a Sytem, La Vega, Nevaa, Octobe 28-3, G. Cao a M. ogo, "AtNet: tbute tgmegetc cotol fo commucato etwo", Joual of Atfcal Itellgece Reeach, vol. 9, pp , G. Cao a M. ogo, "Moble aget fo aaptve outg", Poc. 3t Hawa Iteatoal Cofeece o Sytem Scece, IEEE Compute Socety Pe, Lo Alamto, CA, pp , T. Whte, "Swam tellgece a poblem olvg telecommucato", Caaa Atfcal Itellgece Magaze, Spg, T. Whte, "Routg wth wam tellgece", Techcal Repot SCE- 97-5, Sytem a Compute Egeeg epatmet, Caleto Uvety, Septembe, T. Whte a B. Pague, "Towa mult-wam poblem olvg etwo", Poc. Th Iteatoal Cofeece o Mult-Aget Sytem (ICMAS '98), July, 998, pp T. Whte, B. Pague, a F. Oppache, "ASGA: mpovg the at ytem by tegato wth geetc algothm", Poc. Th Geetc Pogammg Cofeece, July, 998, pp T. Whte, B. Pague, F. Oppache, "At each wth geetc algothm: applcato to path fg etwo", Combatoal Optmzato '98, Buel, Belgum, Apl 5th-7th, 998.

An Approach of Degree Constraint MST Algorithm

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