Copyright 1978, by the author(s). All rights reserved.

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1 Copyrght 1978, by the author(s). All rghts reserved. Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, to republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson.

2 Dstrbuted Query Processng n a Relatonal Data Base System by Robert Epsten Mchael Stonebraker Eugene Wong Memorandum No. UCB/ERL M78/18 17 Aprl 1978 Electroncs Research Laboratory College of Engneerng Unversty of Calforna, Berkeley 94720

3 Dstrbuted Query Processng Page 1 Dstrbuted Query Processng n a Relatonal Data Base System by Robert Epsten Mchael Stonebraker Eugene Wong Electroncs Research Laboratory College of Engneerng Unversty of Calforna, Berkeley Abstract In ths paper we present a new algorthm for retrevng and updatng data from a dstrbuted relatonal data base. Wthn such a data base, any number of relatons can be ds trbuted over any number of stes. Moreover, a user sup pled dstrbuton crtera can optonally be used to specfy what ste a tuple belongs to. The algorthm s an effcent way to process any query by "breakng" the qualfcaton nto separate "peces" usng a few smple heurstcs. The cost crtera consdered are mnmum response tme and mnmum communcatons traffc. In addton, the algorthm can optmze separately for two models of a communcaton network representng respectvely ARPANET and ETHERNET lke networks. Ths algorthm s beng mplemented as part of the INGRES data base system. Research sponsored by the U.S. Army Research Offce Grant DAAG29-76-G-0245, and the Jont Servces Electroncs Program Contract F C-0100.

4 Dstrbuted Query Processng Page 2 I Introducton In ths paper we are concerned wth algorthms for pro cessng data base commands that nvolve data from multple machnes n a dstrbuted data base envronment. These algorthms are beng mplemented as part of our work n extendng INGRES [HELD75, ST0N76] to manage a dstrbuted data base. As such, we are concerned wth processng nteractons n the data sublanguage, QUEL. The specfc data model that we use s dscussed n Secton II. Some of our ntal thoughts on these subjects have been presented elsewhere [STON77, W0NG77]. We are not concerned here wth control of concurrent updates or multple copes [TH0M75, LAMP76, ROTH77, CHU76]. Rather we assume that these are handled by a separate mechansm or can be ntegrated nto our algorthms. Ths paper s organzed as follows: In secton II we formalze the problem by ndcatng our vew of a dstr buted data base and the nteractons to be solved. Then, n secton III we dscuss our model for the computer network. In secton IV a detaled algorthm s presented for handlng the decomposton of queres n a dstrbuted envronment. There are a few complcatons concernng updates and aggre gates n a dstrbuted data base whch are covered n sec tons V and VI. Lastly, n secton VII we draw some conclu sons.

5 Dstrbuted Query Processng Page 3 II The Dstrbuted Data Base Model. We adopt the relatonal model of data [C0DD70, CHAM76] and assume that users nteract wth data through the non procedural query language, QUEL [HELD75]. Algorthms for processng QUEL n a sngle machne envronment (so called "decomposton") have been presented n [STON76, W0NG76]. New algorthms or extensons are needed n a dstrbuted envronment. Some famlarty wth the noton of decompos ton wll be helpful n understandng ths paper. The data base s assumed to consst of a collecton of relatons R, R_,...,R. Each relaton, R., may be at a 1 2 n unque ste or may be spread over several stes n a com puter network. We shall refer to a relaton as beng "local" f t s stored entrely at one ste, and "dstrbuted" f portons of t are stored at dfferent stes. By default relatons wll be assumed to be local unless explctly stated to be otherwse. They can be explctly created (or extended) to be dstrbuted on all or a subcollecton of the stes n the computer network. Call the stes S-, S^,...,S. At a gven 1 2 n ste S. there may be a porton (or fragment [ROTH77]) of R.. Call the porton R'?. We shall assume that each fragment s n fact a subrelaton,.e., a subset of the tuples, of a gven relaton. Hence there s no noton of fragments beng projectons of a gven relaton [R0TH77]. Supportng those more general fragments s nfeasble gven the current structure of INGRES. A dstrbuton crteron, whch determnes how tuples are to be allocated to fragments, may be optonally assoc ated wth each relaton. If no dstrbuton crteron exsts, then tuples wll be placed at the ste where they happen to be processed. Fgure 1 ndcates one collecton of relatons, the fragments that are actually stored and ther dstrbuton crtera. An example query for such a data base s to fnd the job numbers suppled by the sup pler named XYZ. In QUEL ths s expressed as: range of s s suppler range of y s supply

6 Dstrbuted Query Processng Page 4 retreve nto w(y.jno) where y.sno = s.snp and s.sname = "X.YZ" Note that ths query nvolves fragments at all three stes

7 Dstrbuted Query Processng Page 5 Fgure 1 (A sample dstrbuted data base) The users vew: suppler (sno, sname, cty) project (jno, jname, cty) supply (sno, jno, amount) The dstrbuton of Fragments: project suppler where suppler.cty = "Berkeley" ste 1 supply suppler where suppler.cty = "San Jose" ste 3 suppler where suppler.cty!= "Berkeley" and suppler.cty!= "San Jose" III Communcatons Network Model. We are prmarly concerned wth two types of communca ton networks namely ste-to-ste and broadcast networks. In a ste-to-ste network we assume that there s a fxed cost to send one byte of data from any ste to any other ste. In a broadcast network we assume that the cost of

8 Dstrbuted Query Processng Page 6 sendng data from one ste to all stes s the same as that of sendng the same data from one ste to a sngle other ste. Our ste to ste model of a network s motvated by the ARPANET [ROBE70] wth one mportant smplfcaton. In ARPANET the actual cost to communcate between two arbtrary stes wll depend on what route the data must travel.e. on the topology of the network. Our broadcast model s smlar to the ETHERNET [METC76] wth two mportant smplfcatons. We assume that every ste s always free to accept new messages. Thus a message wll never have to be retransmtted because a ste was too busy to accept the message. The ETHERNET restrcts the recpent of a message to be ether one ste or every ste. We assume a more general addressng scheme where anywhere from one to all stes can be addressed n a message. Regardless of whch network model s used, we shall assume that t s desrable to present large blocks of data to the network for transmsson. In other words, bulk transmsson s more effcent. It wll be shown that a broadcast (or ETHER) network s partcularly well suted to a relatonal data base envron ment. The query processng algorthm can take explct advantage of the broadcast capablty of such a network. However, t s our ntenton to have INGRES support a data base on ether type of network.

9 Dstrbuted Query Processng Page 7 IV Query Decomposton. INGRES supports four dfferent data manpulaton com mands: retreve, append, delete, and replace. As mentoned n [STON76], all update commands (append, delete, and replace) are actually processed by convertng them to retreve commands (to dscover what to do) followed by low level fle manpulaton operatons. Thus, the algorthm to decompose queres on a dstrbuted system can be ndependent of the whether t s an update or retreval untl the very end. For ths reason, we shall restrct our dscusson here to "retreves" and cover the relevant problems of updates n the next secton. Optmzaton Crtera. Mnmzng response tme and mnmzng network traffc wll be taken to be the two man optmzaton crtera n a dstrbuted data base envronment. Mnmzng response tme nvolves mnmzng the amount of processng needed to solve a query and usng as much parallelsm as possble from the varous computer stes. Mnmzng network traffc nvolves transmttng only the mnmum data needed to solve the query. These two crtera are not unrelated. An ncrease n network traffc wll mprove response tme f t results n greater parallel processng. Network Decomposton Algorthm. We frst present the skeleton of the bass algorthm. We subsequently dscuss the detaled optmzaton tactc nvolved. The algorthm to decompose a query has the followng nputs: 1) the conjunctve normal form of the query (.e. the qualfcaton s a collecton of clauses separated by AND's; each clause contanng only OR and NOT). 2) the locaton of each fragment and ts cardnalty. 3) the network type (ste-to-ste or broadcast). The algorthm s presented wthn the flowchart n Fgure 2. The partcular ste where the query orgnates s called the

10 Dstrbuted Query Processng Page 8 "master" INGRES ste. The master INGRES communcates wth one "slave" INGRES at each ste that s nvolved n process ng the query. These "slaves" can be created by the "mas ter" when approprate. There are two types of commands that a master INGRES can gve to a slave INGRES. 1) run the (local) query Q. 2) move the (local) fragment R. of relaton R to a sub set of the stes n the network, S-. S0,..., S. ' 1' 2' ' m The algorthm proceeds as follows: (1) Do all one varable sub-queres. Ths has been shown n [YOUS78] to be almost always a good dea for nondstrbuted data bases. It should be equally true for ds trbuted data bases. Note that n the example query from secton II, a one-varable subquery: we have range of s s suppler retreve nto temp(s.sno) where s.name = "XYZ" In step (1) the master INGRES at the ste where the query orgnated nstructs a slave at each of the three stes to run the above subquery. The result s a fragment of temp at each ste. The orgnal query now becomes: range of t s temp range of y s supply retreve nto w(y.jno) where y.sno = t.sno Before actually runnng such a subquery, f the rela ton has a dstrbuton crteron, check to see f a clause n the dstrbuton crteron at ste contradcts a clause n the subquery. In general ths requres a propostonal calculus theorem prover. However, there are some smple cases for whch contradcton s easly determned. For example, f the user's query ncludes a clause such as... and suppler.cty = "San Francsco" examnng the dstrbuton crteron for ste mght show

11 Dstrbuted Query Processng Page 9 Fgure 2 start yes none Do all 1 varable queres on all stes Elmnate stes f possble. v Was there a 1 varable query whch was false on all stes? I no v Apply reducton algorthm j < v < Choose "next pece" of query, v Can "pece" be done yes on sngle stes?! no v Select processng stes and varables to transmt Transmt varables Run Query(es) All False?. no! yes v Done

12 Dstrbuted Query Processng Page 10 suppler where suppler.cty = "Berkeley" Thus wthout actually runnng the sub-query on ste, the porton of suppler on ste can be elmnated from the query. (2) If there s a sub-query that was not satsfed on any ste n (1), the entre query s false and we are done. Ths would happen n our example f temp had no tuples at all stes. (3) Apply the reducton algorthm [WONG76] to the query. Ths wll recast the orgnal query nto a sequence of com ponent queres, each of whch s processed n order, ndependently. Consder a query Q(x1,x2,- -.,x ) n QUEL where each varable x references a relaton R.. Q s sad to be redu cble f t can be replaced by a sequence of two queres (Q'» Q") that overlap on only one varable,.e., Q( xr x2,... xn) > Q'( xm, xn+1,... xn) followed by Q"( x1 x..., x' ) 1,2, m where the range of x' s the result relaton of Q'. For example the query: range of s s suppler range of y s supply range of j s project retreve (s.sname) where s.sno = y.sno and y.jno = j.jno can be reduced to two components namely: retreve nto temp (y.sno) where y.jno = j.jno followed by

13 Dstrbuted Query Processng Page 11 range of t s temp retreve (s.sname) where s.sno = t.sno It s shown n [WONG76] that the rreducble components of a query are unque, and an ntutve argument s presented whch ndcates that these components form an advantageous sequence of subqueres. To test ths hypothess,.expermentaton wth actual data was recently undertaken by [YOUS78] and the results were convncngly affrmatve. It should be equally advantageous n a dstr buted system. Ths step wll perform the reducton algorthm and arrange the rreducble components of the query n ther unque sequence. We can then consder the subqueres ndependently. The example query from secton II s not reducble so ths step has no effect. (4) Choose the "next pece" of the query to process. A query conssts of a target lst and a qualfcaton (whch s n conjunctve normal form). We defne a "pece" as one or more clauses and ther assocated target lsts. Based on the query structure and the sze and locaton of the fragments, the next "pece" of the query to be pro cessed s selected. The algorthm to do ths wll be explaned shortly. In our example there s only one reman ng clause, whch therefore must be the next pece. (5) If the pece to be run can be done on ndvdual stes wthout movng portons of the relatons, then we proceed to step (9). In our example temp s at three stes and supply s at one. Hence, data must be moved n order to proceed. (6) Select the ste(s) that wll process the next pece of the query. Dependng on the number of stes, and whether t s a ste-to-ste or broadcast network, anywhere from one to all possble stes may be chosen. Suppose for our example that all three stes are chosen. (7) The sub-query must be two varable or more n order to reach ths step. In order to process an n varable subquery, fragments from n - 1 relatons must be moved, and the remanng relaton wll reman fragmented. Each ste

14 Dstrbuted Query Processng Page 12 that does processng must have a complete copy of the n - 1 relatons. If processng s done on a sngle ste, t must have copes of all n relatons. For our example we can broadcast supply to all stes. Each ste wll then have all of supply and a fragment of temp and wll process the query producng a local fragment w. The answer to the query s the dstrbuted relaton w. Alternatvely, we can choose to broadcast temp to all stes nvolved n the query. Here we can vew supply as dstrbuted but wth zero tuples on two of the three stes. Hence, fragments of temp wll be sent to ste 2. Ste 2 then processes the same local query as above to produce a w; whle stes 1 and 3 have no work to do. Lastly, we can choose to equalze the dstrbuton of the tuples n the relaton that remans fragmented so as to guarantee that all processng stes have the same amount of work to do. Ths requres sendng each ste a complete copy of temp, and movng one-thrd of the suppler tuples to each of the other two stes before proceedng as above. (8) Move the selected relaton fragments to the selected stes. Each ste wll be drected, n turn, to send a copy of ts selected fragments to the stes selected n step (6). An optmzaton here s to have each ste send only the domans needed n the query. Thus a fragment can be pro jected and duplcates removed. Ths step can take full advantage of a broadcast net work snce we are often broadcastng from one ste to many stes. (9) The master INGRES now broadcasts the query to the selected stes and wats for all stes to fnsh. Once the query has been transmtted, ths step nvolves only local processng. If no ste fnds the qualfcaton to be true, then we know the query s false and no further processng need be done. Otherwse the clauses just run are removed from the query and the new range of the remanng varables s changed f necessary.

15 Dstrbuted Query Processng Page 13 (10) Go to step (4) The Optmzaton Problem. As outlned n the flowchart, the processng algorthm that we have chosen nvolves several decsons: (1) What s the "next pece" of the query that should be processed? (2) Whch stes should take part n the processng of that pece? (3) If the number of partcpatng ste s greater than one, whch of the relatons should be left fragmented? (4) Should the fragmented relaton be equalzed n sze among the processng stes? Choosng the "Next Pece". We have chosen to solve a query by "dvde and con quer". That s, a query wll be broken nto one or more parts and each part wll be processed n turn. The algo rthm we pursue can justfably be called a "greedy" algo rthm. We wll try to optmze each step, ndvdually, wthout explctly lookng ahead to examne the global consequences. A possble refnement s to consder the structure of the resdual query when decdng what should be done. The trade off between cost and beneft remans to be studed. Results from decomposton on a sngle ste have shown that reducng a query nto ts rreducble components s a good heurstc. Thus, after all one varable subqueres have been removed, the reducton algorthm wll be used to transform the orgnal query nto ts rreducble components whch overlap on none, or one varables. Q -» Kr K2,..., K± We could stop at ths pont and smply execute each com ponent n order, whch s what we do on a sngle ste. How ever, snce any one component may span multple stes, t may be desrable to subdvde further. Every component con tans one or more clauses: K = C.., Cp».» C. The queston s whether we should process the entre com ponent at once or subdvde t? The answer s to subdvde

16 Dstrbuted Query Processng Page 14 only f the sze of the result relaton from subdvdng s smaller than the communcaton cost of transmttng the source relatons needed to process t. Here s an example to ntutvely llustrate what can be acheved. Consder the database from secton II wth relatons: suppler (sno, sname, cty) project (jno, jname, cty) supply (sno, jno, amount) and the query: "fnd the names of suppler-project pars such that the suppler supples the project and the two are n the same cty." In QUEL ths can be stated as: range of s s suppler range of j s project range of y s supply retreve (s.sname, j.jname) where s.cty = j.cty and s.sno = y.sno and j.jno = y.jno Ths query s rreducble and nvolves three varables. There s only one rreducble component (namely the entre query) and t nvolves three clauses. To keep the example smple we shall gnore ste 3 from Fgure 1 and pretend there are only two stes, whch have: ste 1 ste 2 project (200 tuples) supply (400 tuples) suppler (50 tuples) suppler (50 tuples) Assume that the tuples of the three relatons have the same wdth. Now consder the costs and benefts of subdvdng the component. We need to examne the four possble choces: (Q1) retreve nto temp(s.sname, s.cty, y.jno) where s.sno = y.sno

17 Dstrbuted Query Processng Page 15 (Q2) retreve nto temp(s.sname, s.sno, j.jname, j.jno) where s.cty = j.cty (Q3) retreve nto temp(j.jname, j.cty, y.sno) where j.jno = y.jno (Q4) retreve (s.sname, j.jname) where s.cty = j.cty and s.sno = y.sno and j.jno = y.jno These are the only possble alternatves. Choosng any two clauses would be tantamount to Q4 snce any two clauses nvolve all three relatons. Q4 would requre movng 200 project tuples and 50 sup pler tuples at whch pont we could complete the query. Therefore, any subdvson wll have to do better than that. Suppose we choose to do Q1. Ths would requre movng 50 suppler tuples. The result relaton would have to be moved n order to process the remanng query: range of t s temp range of j s project retreve (t.sname, j.jname) where t.cty = j.cty and j.jno = t.jno If s.sno were a unque dentfer for suppler and each sup pler suppled only one job, then the result from Q1 would be at most 50 tuples. Thus the total network cost would be movng 50 suppler tuples followed by at most 50 tuples of temp. But also consder the worst case. Suppose that sno s not unque and the entre cross-product of suppler and sup ply f formed. It would have 50 * 400 = 20,000 tuples! The decson whether to subdvde a component must be based on the expected sze of the result relaton. Some method for estmatng the result sze s needed. But suppose the worst happens and the result sze explodes geometrcally. We can throw the result away and smply revert to runnng the whole component. In that case

18 Dstrbuted Query Processng Page 16 we would lose the tme spent processng the abandoned query. The accuracy of estmatng the result sze depends on a careful examnaton of the semantc content of the query (e.g., whether a clause nvolves an equalty), on nforma ton concernng the dstrbuton of values of the domans, (e.g., sno may be a prmary key for the suppler relaton wth no more than one tuple for each possble value), and on the number of varables n the target lst and ther szes. Whle complng and keepng extensve statstcs s mprac tcal, a value ndcatng whether a doman s nearly a pr mary key or not may be both useful and easy to keep. Determnng How to Process the "Next Pece". The second part of the optmzaton problem s how to process a gven subquery. That s, whch stes should be used as processng stes and whch relaton fragments should be moved. The more stes nvolved, the greater the paral lelsm. However, usng more stes may nvolve greater com muncaton costs and delays. Presumably we wll want to make decsons whch mnm ze some applcaton dependent cost functon whch mght look somethng lke: F(c1 * network_communcaton + c2 * processng tme) To do ths we wll need to know how to calculate the amount of network traffc nvolved, the relatve processng tme, and the cost/benefts of equalzng the fragmented relaton. We wll now proceed to explan how to determne each of these. Notatonally, we know there are: N total stes n the network n relatons referenced n the "next pece" We need to choose: K stes to be processng stes R as the relaton to be left fragmented Let's number the processng stes so that 1 <= j <= K. Furthermore, let's defne M. as the number of stes where R.

19 Dstrbuted Query Processng Page 17 has data stored nvolvng At each processng ste j we have a query Qj = Q(R1, R2' ' ^p' ' ',R n ) Determnng Network Cost Gven R and K. Assumng that one relaton R s left fragmented, and K stes (out of N) partcpate n processng, then the frag ments of R. have to be moved as follows: for a processng ste j, R^ s moved to K - 1 other stes. for a non-processng ste j, Rv s moved to K other stes and any fragments of R^ are moved to any one processng ste. The total communcaton cost s gven by comm = K 2 c!rj!! J=1 K-1 [_^p ' ll J=K+1L IRj"j!CKLT_- *P l 3-I n J l L. C- R f 1 l_l P 1-1 l where C (x) denotes the cost of sendng x bytes of data to K stes, a cost that depends on the network that s used. Estmatng Relatve Processng Tme. Defne proc(q) to be the tme requred to process the query Q f t were done on a sngle ste. If K s greater than one then the processng tme of a query, Q, can be mproved from proc(q) to max. proc(q.). In other words, the processng tme for the whole query s equal to the process ng tme of the ste j wth the most processng to be done. It s reasonable to assume that the processng tme at each ste s gven by procq. J R Jl proc r n so that the overall processng tme s

20 Dstrbuted Query Processng Page 18 1 n trj max proc jq. = max"1 tl proc r ~,Q j 1 " 1' j!r! J! P! assumng that all stes are of approxmately equal process ng speed. Cost for Equalzaton. If each fragment of R was the same sze, then the overall processng tme would be gven by 1/K proc(q), snce each fragment would have (1/K) of the data. (Ths assumes, agan, that all computer stes are of approxmately equal speed.) Ths s the motvaton for equalzaton. To determne the cost of equalzng, let us defne the functon pos(x) to be: f x > 0 then pos(x) = x f x <= 0 then pos(x) r 0 The amount of data to be moved n equalzng the fragments of R s gven by N 2 pos RJ - R j L P NJ p. j=1 Ths added network RJ mprovement from - trade some network cessng tme. R P CO' cost would result n processng to j7. Thus t may be desrable to st for an mprovement n overall pro- We now know how to compute network communcaton cost, relatve processng tme, and the cost and beneft of equal zng R We wll now use ths knowledge to mnmze some example cost functons Mnmzng Communcaton Costs. For the moment let's assume that the overall optmza ton crtera s to mnmze communcaton costs. It s mportant to treat ste-to-ste and broadcast networks separately. We wll frst consder usng a broadcast

21 Dstrbuted Query Processng Page 19 network and solvng for K and R. For a broadcast network CK(x) = C^x) for all K >= 1. By examnaton of the communcaton cost functon gven on page 17 t can be seen that the communcaton cost functon s always mnmzed by K = 1 or K > M. To see ths observe that the cost functon has three terms. The frst term wll be zero f K = 1. The thrd term wll be zero f every ste whch has part of R s a processng ste. Thus K must be > M, where M s the number of stes where R_ s present. - p' p P If we assume that C^x) s lnear n x and rearrange some terms then rcomml. ahna. = cjslr,] - lwa\ for K=1 L J broadcast 1 - l} ^ 11 Hence, ICOMM j J. = cj5»r.'-'r'! for K=N LUU1,UJ broadcast 1jfj. P j L. -I the decson rule for mnmzng communcaton n the broadcast network case s gven by If max SR^ > max»r., choose K = 1 and choose the 1 ' 1 I ' processng ste (ste 1) to be the one contanng the most data. In ths case there s no R. In other words, f one ste has more data than the largest relaton, then K = 1 and choose that ste. If max 2R- < max R.j, choose Rrt to be the relaton J l ll! X P contanng the most data and choose K=M. The stuaton for ste-to-ste networks s qute df ferent. For that case we shall assume C^(x) = k Cj(x) and that C-(x) s agan lnear n x. We note that, ndependent of K the choce of R that mnmzes communcatons s the P ' relaton wth the most data,.e., max jr. ]. Once R s chosen, the value of K that mnmzes communcatons s determned as follows: Let the stes be arranged n decreasng order of? R^. Then, choose K to be 1 f 1 ll

22 Dstrbuted Query Processng Page 20 1 Rj - lr-! > \K\ otherwse choose K to be the largest j such that 2 R, - IR^I! < R^ ^p 1 I 1 l-j I P I The nterpretaton of ths decson rule s as follows. A ste should be chosen as a processng ste f and only f the data that t s to receve as a processng ste s less that the addtonal data that t would have to send as a nonprocessng ste. If mnmzaton of communcaton cost s the sole cr teron of optmzaton, then the best choces for both K and R have been completely determned for both broadcast and p ste-to-ste networks. We expect the followng exceedngly smple rule to be reasonable for choosng the number of pro cessng stes: Choose R to be the largest relaton. P f N = 2 and n = 2 then K = 2 f N 2 then K = M for broadcast network K = 1 for ste-to-ste network Mnmzng Processng Tme. Suppose for the moment that our goal was only to mnm ze processng tme and we were wllng to gnore any net work costs or delays. In ths case we would want K = N so that we could dstrbute the work among all stes. We would stll need to choose one relaton to reman fragmented. The actual processng tme wll be ndependent of whatever rela ton we choose. To see ths notce that when we equalze the fragmented relaton the processng tme goes from RJ ' n' 1 max. J tllproc(q) to - proc(q), whch s ndependent of R. J Sr! K y! P!

23 Dstrbuted Query Processng Page 21 Snce we can choose any R our choce for R should be the relaton whch mnmzes network traffc. Thus we are lookng for R whch mnmzes: P 2 c 2 rj j + 2 pos! rj - /njrd;! j=1 N-1_*p' 1,j j=1 "- ' p» p J Summary. The true optmal soluton cannot be determned wthout knowng the precse relatonshps between processng tme and communcaton costs, the dstrbuton of data among the N stes, and the true processng tme for each ste. Any optmal soluton would have to consder the possblty of usng any value of K from 1 to N. Exactly how to choose R and K s an open ended ques ton untl the cost crtera have been specfed. We have shown solutons at two extremes (mnmum network traffc and mnmum processng tme). Note the smlarty between the "next pece" decson and the next tuple varable to be chosen for substtuton n sngle ste decomposton. The same nablty to acheve a true optmum s present n both cases. Just as refnement of the decson makng process was presented n [YOUS78] for decomposton, we plan to do expermentaton concernng cases where each possble algo rthm s best.

24 Dstrbuted Query Processng Page 22 V Updates. INGRES wll be expanded to allow dstrbuted relatons wth optonal dstrbuton crtera. When nserts occur they can cause tuples to be placed on specfc stes. In the case of a replace command, they can cause tuples to be moved from one ste to another. We wll assume that a dstrbuton crteron maps a tuple to a unque ste or to no ste at all. It s possble that a crteron dsallows certan values. Snce the ds trbuton crteron s related to an ntegrty constrant [STON75], tuples whch cannot belong to any ste could be treated as a volaton of an ntegrty constrant. Wth a dstrbuton crteron we wll guarantee that the collecton of all the fragments of a relaton contans no duplcates. Wthout a dstrbuton crteron, any one fragment wll contan no duplcates, but the collecton of all stes can contan duplcates. To support any other rule seems too costly. The processng of an update wll proceed as follows: (1) At the end of the query decomposton, one or more stes wll have a porton of a temporary relaton that holds the changes to be made to the result relaton. (2) Each ste performs the updates specfcally desg nated for t. (3) The remanng updates (f any) are sent drectly to ther correct stes. (4) Each ste completes any new updates receved. The decomposton algorthm can help the update pro cessng by never movng the result relaton. For example, n the query: range of p s project range of s s suppler delete p where p.cty = s.cty decomposton has the choce of movng ether p or s. By

25 Dstrbuted Query Processng Page 23 always choosng NOT to move p (the result relaton var able), we optmze the update processng. Ths s because step (3) above wll then have no tuples for other stes. However, choosng not to move the result relaton, may be a poor tactc durng decomposton. The trade-off cannot readly be determned wthout advance knowledge of how many tuples of the result relaton satsfy the qualfcaton. We wll now dentfy what must be done for each update command, wth or wthout a dstrbuton crteron. For an append command, each tuple to be appended s put nto a temporary relaton and then splt accordng to steps (1) to (4) above. If there s no dstrbuton crteron, the tuples can be appended drectly nstead of gong through a temporary relaton. For a delete command, the temporary relaton conssts of a tuple dentfer (TID) and machne dentfer (MID). The algorthm s the same regardless of the dstrbuton crteron. Note that f we guarantee that the result rela ton s not moved durng decomposton, we do not need the MID. The set of TIDs s only for the machne n whch they resde. In fact, f the result relaton s not moved durng decomposton, the temporary relaton s not needed. The deletes can be done drectly. For a replace command, the TID, MID, and the new tuple must be saved. If the relaton does not have a dstrbuton crteron the replace command s processed n the same manner as a delete. Wth a dstrbuton crteron, t s possble that a tuple wll have to be moved from ts current ste to another. If ths happens, t must be deleted at the current ste and marked to be appended at ts new ste. If decomposton moves the result relaton and a tuple has to change stes because of a replace, steps (3) and (4) must be repeated twce. In order to provde for recovery from a system crash durng an update, updates are not done drectly, nstead we use a "deferred update" fle [STON76]. The deferred update fle wll contan a full mage of all changes that must occur before any actual updates take place. The deferred update mechansm s hdden below the mechansm we have been dscussng.

26 Dstrbuted Query Processng Page 24 All update processng s controlled by the master INGRES. The ndvdual stes can all perform the updates n parallel. If the result relaton s never moved durng decomposton, addtonal network costs can only occur n append, and replace commands where the dstrbuton cr teron forces the tuples to be moved to a new ste.

27 Dstrbuted Query Processng Page 25 VI Processng of Aggregates. The current mplementaton of INGRES processes aggre gates (mn, max, avg, sum, and count) frst and then decom poses the remanng aggregate-free query. Although ths s not always optmal, t typcally s and t s a smple query processng strategy. For dstrbuted INGRES we also plan to process all aggregates frst. Some optmzaton specfc to aggregates can be done. For example, aggregates that range over only one relaton, and are done wthout removng duplcates are processed on ndvdual stes and the aggregated results are transmtted back to the master ste where they are combned to produce the fnal result. Aggregates whch nvolve more than one relaton or whch requre duplcates to be removed, are processed by frst retrevng the values to be aggregated nto a dstr buted temporary relaton, and then aggregatng on that tem porary relaton. If the aggregate requres duplcates to be removed, then the temporary relaton wll have to be col lected onto a sngle ste n order to remove duplcates. Other optmzaton technques such as processng as many aggregates as possble n the same pass through the relaton, and optmzng the by-domans references n aggre gate functons, wll contnue to be performed.

28 Dstrbuted Query Processng Page 26 VII Conclusons. The model we propose for a dstrbuted data base s very flexble. Portons of a relaton can exst at any number of stes and an optonal dstrbuton crtera can be used to assgn tuples to specfc stes. The algorthm for decomposng a query nvolves examn ng the structure of a query's qualfcaton. The query s processed by choosng for processng one or more clauses of the qualfcaton at a tme. It s nevtable that some data wll have to be moved from ste to ste n order to process a query. The algorthm tres to move only the smal lest amount of data, and tres to get the maxmum amount of parallel processng possble. In addton, by tryng to avod movng the result relaton, we help to optmze the update processng. Durng query processng t s frequently desrable to broadcast data from one ste to several other stes, whch makes a broadcast network extremely desrable.

29 Dstrbuted Query Processng Page 27 REFERENCES [CHAM76] Chamberln, D.D.; "Relatonal Data Base Manage ment: A Survey," Computng Survey, Vol. 8, no. 1, March [CHU76] Chu, Wesley W. ; "Performance of Fle Drectory Systems for Data Bases n Star and Dstrbuted Networks," AFIPS Conference Proceedngs, vol. 45, [CODD70] Codd, E.F.; "A Relatonal Model of Data for Large Shared Data Banks," CACM vol. 13, no. 6, June [HELD75] Held, G.D., M.R. Stonebraker, and E. Wong; "INGRES - A Relatonal Data Base System," Proc. NCC vol. 44, [LAMP76] Lamport, L.; "Tme, Clocks and Orderng of Events n a Dstrbuted System," Mass. Computer Assoc ates Report CA , March [METC76] Metcalf, R. M. and D. R. Boggs, "Ethernet: Ds trbuted Packet Swtchng for Local Computer Net works," CACM, vol. 19, no. 7, July [ROBE70] Roberts, L. and Wessler, B., "Computer Network Development to Acheve Resource Sharng," Proc. SJCC, 1970, AFIPS Press. [ROTH77] Rothne, J.B. and N. Goodman; "An Overvew of the Prelmnary Desgn of SDD-1: A System for Ds trbuted Databases," 1977 Berkeley Workshop on Dstrbuted Data Management and Computer Net works, Lawrence Berkeley Laboratory, May [STON75] Stonebraker, M.R.; "Implementaton of Integrty Constrants and Vews by Query Modfcaton", Unversty of Calforna, Electroncs Research Laboratory, Memorandum ERL-M514, March 1975.

30 Dstrbuted Query Processng Page 28 [STON76] Stonebraker, M.R., E. Wong, P. Kreps and G.D. Held; "Desgn and Implementaton of INGRES," ACM Trans. Database Systems, vol. 1, no. 3, Sept [ST0N77] Stonebraker, M.R. and E. Neuhold; "A Dstrbuted Database Verson of INGRES," 1977 Berkeley Workshop on Dstrbuted Data Management and Com puter Networks, Lawrence Berkeley Laboratory, May [TH0M75] Thomas, R.H.; "A Soluton to the Update Problem for Multple Copy Databases Whch Use Dstrbuted Control," BBN Report 3340, Bolt Beranek and New man Inc., Cambrdge, Mass., July [W0NG76] Wong, E. and K. Youssef; "Decomposton - A Strategy for Query Processng," ACM Trans. Data base Systems, vol. 1, no. 3, Sept [W0NG77] Wong, E. ; "Retrevng Dspersed Data from SDD-1: A System for Dstrbuted Databases," 1977 Berke ley Workshop on Dstrbuted Data Management and Computer Networks, Lawrence Berkeley Laboratory, May [Y0US78] Youssef, K. ; "Query Processng for a Relatonal Database System," Ph.D Dssertaton, Unversty of Calforna, Berkeley, 1978, Electroncs Research Laboratory, Memorandum UCB/ERL M78/3, January 6, 1978.