Physical Design of Network Model Databases Using the Property of Separability

Transcription

1 Physica Design of Network Mode Databases Using the Property of Separabiity Kyu-Young \?hang* Gio Wicdcrhod Danie Sagaowicz Stanford University SRI Internationa Abstract A physica design methodoogy for network mode databases is dcvcopcd using the theory of separabiity. In particuar, a arge subset of practicay important access structures provided by network mode database systems is shown to have tic property of separabiity under the usage specification schcmc proposed. The theory of separabiity was introduced in an caricr work, in the context of reationa systems, as a forma basis for partitioning the probem of designing the optima physica database. The theory proves that, given a certain set of access structures and a usage spccitication scheme, the probem of optima assignment of access structures to the cntirc database can be reduced to the subprobem of optimizing individua record types indcpcndcnty of one another. The approach prcscntcd significanty rcduccs the compexity of the design probem which has the potentia of being combinatoriay exposive. 1. Introduction Performance is an important issue in designing databases. As a resut, the probem of physica database design has been given much attention in rcccnt years. This probem concerns finding an optima configuration of physica fies and access structures-given the ogica access paths that rcprcscnt the intcrconncction among objects in the data modes, the usage pattern of those paths, the organizationa charnctcristics of stored data, and the various features provided by a particuar database management system (DBMS) [HSI 701 [CAR 751[SCH 751 [SEV 751 [HAM 761 [YAO 771 [BAT 801 [GER 771 [CAM 771. Throughout this paper, we use the term access sfrucfure as a generic term for both access methods (e.g., indexes) and storage stucturcs (c.g., various strategies for the paccmcnt of records) that a particuar DBMS provides. In the physica database design, access structures are spccificd to support ogica objects (such as record types or the entire database) in the database. WC use the term access cottjguru~iot~ of a ogica object to mean the agrcgate of access structures specified to support that ogica object. *Authors current addresws: Compukr Systctiu 1 abon~ory. Dcpxmcnts of Eccrira I:nginccrin!; and C ompucr Scicncc. Skmford IJnivcrsiy, SIanford, CA , and Ariicia Intcigcncc Ccntcr, SItI I~~fcrnaioua, Mcn!o I at. CL\ In the past, most of the rcscarch on this subject concentrated on rather simpe casts deaing with a singe fie; in many casts, such a fie rcprcscnts the storage structurc for one ogica object (such as a reation in the reationa mode or a record type in the network mode). In a database organization, howcvcr, the access configurations for many ogica objects have compex intcrrcationships and access patterns. A simpe extension of singctit anayses does not suffice for understanding the interactions among ogica objects. Some efijrts have been dcvotcd to the casts of mutipe ogica objects [GER 771 [BAT SO] [KAT SO]. The approaches cmpoycd, however, cithcr fa short of accompishing automatic design of optima physica databases or provide ony genera, not quantitative methods. Cost modes wcrc deveoped in [GER 771 and [BAT SO], but it is difficut to use them for the optima design of physica databases without an exhaustive starch among a possibe access configurations of the database. (A method based on heuristic pruning of the starch space has been reported in [SCH 791.) As pointed out in [GI:R 771, a rccvant partitioning of the entire design is necessary to make the optima design of physica databases a practica matter. The theory of separabiity, which was used in PHI\-a 811 for the physica design of reationa databases, can be empoyed for network mode databases as we. The theory proves that, if certain conditions arc satisfied, the probem of designing the optima physica database can bc rcduccd to the subprobcm of optimizing individua record types indcpcndenty of one another. Once the probem has been partitioned, the techniques dcvcopcd for singefie designs can bc appied to sove the subprobems. The conditions to bc satisfied. howcvcr, arc genera in nature, and their detais must bc anayzed for individua systems to bc considered. WC sha dcvcop, in this paper, a physica design methodoogy for network mode datnbascs using the property of separabiity. Since network mode database systems provide diffcrcnt variety of access structures and have diffcrcnt characteristics (e.g., they are more procedura in nature) than reationa systems do, we need to set up a fairy different framework (cspcciay usage specification) for the deveopment of a design methodoogy. Therefore, we sha put emphases on deveoping a usage spccitication scheme. that is suitabe for describing the network mode database environment and on proving that, under this usage spcciication schcmc, a arge subset of practicay important acces structu,rp that arc avainbc in Proceedings of the Eighth Internationa 98 Mexico City, September, 1982

2 network mode database systems satisfies the conditions for separabiity. This design proccdurc based on the property of separabiity wi then 6c extended, using heuristics, to incude oticr access structures that arc not considcrcd initiay. WC discuss the issues invoved in designing the access configuration of a physica datrbase so as to minimize the number of disk accesses for a set of read and update transactions that act upon it. We choose the system specification given in the Journa of Dcvcopmcnt of CODASYL Data Description Language Committee [COD-a 781 and that of CODASYL Cob01 Committee [COD-b 781 (CODASYL 78 Database Specification) as our environment. Fcaturcs provided in this report wi be bricty introduced in Section 2. Section 3 introduces key assumptions, whie Section 4 dcscribcs the principe of separabiity and the design theory. A design agorithm based on the theory wi be introduced in Section 5. Extensions of our approach are mcntioncd briefy in Section CODASYL 78 Database Specification In this section, we introduce the features provided by the CODASYL 78 Database Specification. (We use the 78 dcicription to hande a broader spectrum of access structures that may be used in network mode database systems. The 71 version can be treated in a simiar but easier way.) In this new specification, theconcept of storage schema has been introduced to scparatc many storagereated aspects from the conceptua schema. The storage schema is defined by using the Data Storage Description Language (DSDL) which is separate from the Data Description Language (Schema DDI.). Among many new features. the foowing ones are of interest in the physica database design: (Note that the DSDL in [COD-a 781 was ony a proposed draft. In our discussion, however, we keep using this version as a mode for network mode database systems.) *The schema DDL now aows mutipe record keys to be defined for each record type. A record key is caed a recordorder& key if an order is defined for it by specifying ASCENDING or DESCENDING. o Indcxcs can be dcfincd in the storage schema to support the record keys spccificd in the conceptua schcnu Indexes can aso be used to rcprcscnt a SET type, i.c., as pointer arrays. (Throughout this paper, the term Sfi7 wi bc used to mean a DBTG set.) e A seria scan of a the records of a record type is possibe by specifying a record-order key in the subschcma. which in turn shoud be mapped to a record-ordering key in the conceptua schema. Ony one record-order key can bc dcfincd in the subschcma. Seria order hcrc impies ony a ogica ordering and does not necessariy mean that the records arc actuay stored scqucntiay. hc paccmcnt of a record (ocation mode in caricr terms) can be done in any one of thr& different ways. (We ignore secondary options such as DISPLACEMRN I or WITI-I in the DSDL.) A record can be 3. Assumptions o Paced according to a CALC key, o Custered via a SET dcfincd in the conccptia schema, and, optionay paced near the owner, o Stored sequentiay in ascending or descending order according to the vaue of a set of data items. In this section, we summarize the key assumptions that wi be used throughout the paper. The database is assumed to rcsidc on diskike devices. Physica storage space for the database is divided into fixed-sijrs: units caed bocks [WIE 771. The bock is not ony the unit of disk aocation, but aso the unit of transfer between the main memory and the disk. We assume that records of a types are stored in one area, and that they are randomy scattered therein. It is assumed that the custering of records of the mcmbcr type of a SET affects the reative distances between records of that type, but does not affect the distances between records of other types. To.make this assumption vaid, we excude the custering of member records near their owner record. We assume that the CALC records are randomy distributed, and that the average number of bock accesses required to access one record by CALC key is the same for any record type and for any key, depending ony on the overa oad factor of the area. We ignore any disparity in the size of records of the owner type of a SET that resuts from various SET impementations, SO that a SET impementation affects the size of member records ony (because of the space needed for additiona pointers). Furthermore, if an index is used to represent a SET occurrence, it is assumed that this index is not stored near the owner record (i.e., the NEAR OWNER option for the pacement of index entries is cxcudcd from our consideration). A mutimcmbcr SET and other options, such as sorted SETS, wi not be considered. 4. Design Theory In this section, WC dcvcop the design theory based on the concept of separabiity. Specificay, we introduce the forma definition of separabiity, formuate the partia-operation cost, and show that the mode system (which wi be defined in Section 4.2) consisting of a subset of access structures in CODASYL 78 1)atahase Specification, satisfies the separabiity under the assumptions WC made in Section 3 and tbc usage specification we Proceedings of the Eighth Internationa Mexico City, September, 1982

3 sha dcvcop. A cost mode simiar to the one devcopcd by Gcrritscn [GER 771 is introduced as an exampe of a separabe system. ;inay, update costs are discussed briefy. 3. Indexes 4. Singuar SETS 5. Record-order key 4.1. Theorem of Separabiity 6. Various SEX impcmcntations Definition 1: The procedure of designing the optima access configuration of a network mode database is separabe if it can be dccomposcd into the tasks of designing the optima configurations of individua record types indcpenddnty of one another. 0 Definition 2: A parfia-operafion cost of a transaction is that part of the transaction-processing cost that reprcscnts the accessing of ony one record type, as we as of the auxiiary access structures defined for it. C We consider various SET impementations to be the access.structures that beong to their member record type. Accordingy, the access cost of owner records, when they are accessed through the SET, wi be incuded in the partia-operation cost for the member record type as shown in Equation 5. Definition 3: A partia operafion is a conceptua division of the transaction whose processing cost is a partia-operation cost. C Theorem 1: The procedure of designing the optima access. configuration of a network mode database is separabe if the foowing conditions are satisfied: 1. The partia-operation cost of a transaction for a record type can be determined regardess of the access configuration specified for and the partia operation used for the other record types. 2. A partia operation for a record type can be chosen regardess of partia operations used for the other record types. Proof: Condition 2 states that, in seecting a partia operation of a transaction for a record type, we are not constrained by the partia operations chosen for the other record types. Furthermore, since a partia-operation cost of a record type is not affected by the access configurations of and the partia operations used for the other record types, ncithcr the specific access structures assigned to one record type nor the partia operation used for it can affect any design parameters for other record types. It is therefore guaranteed that there wi be no interference among the designs of individua record types. 0 a. Link with next pointer b. Link with next pointer and prior pointer c. Link with next pointer, prior pointer, and owner pointer d. Link with next pointer and owner pointer e. SET impementation by index (pointer array) Athough a singuar SET is specified in the conceptua schema, it is an option that can be used to improve the performance. Thus, WC view it here as an acces structure avaiabe for the physica database design. The record-order key defined in the subschema is ikewise regarded as an acces structure. The pacement strategies 1. SEQUENTIAL 2. CLUSTERED VIA SET NEAR OWNER are not incuded here, since, in the foowing situations, a condition for separabiity is not satisfied: Situation 1: In Figure 4-1 we have two record types, R, and R, that are the owner and the member types, respectivey, of SET type S. The symbo - - * in the figure reprcscnts a SET type and the asterisk refers to tic member record type. It is desired, whie a transaction is being processed, that SET type S be travcrscd from R, to R, for every record in R,, and that the R, records be scanned according to their physica order. The R, records arc stored sequentiay (by the SEQUENTIAL option) according to the vaues of the data items whose vaues determine the set membership (inking data items). (Linking data items correspond to the join attributes in reationa terms.) j R I --L-* j R Access Structures in the Mode System Our mode incudes the foowing acces structures: 1. Pacement by a CALC key 2.Paccmcnt by CLUSTERING VFA SET (but not NEAR OWNER) Figure 4-1: Record Types R,, R, and SET Type S between Them In this situation, the order of accessing the records of R, wi bc random if R, records are not stored scqucntiay (by the SF,QUEN I hl option) accbrding to the vaues of the inking data Proceedings of the Eighth Internationa 100 Mexico City, September, 1982

4 items. Randomy accessing R, records wi resut in approximatey one bock access for cvcry record of R,. I Iowcvcr, if the records of R, arc stored scqucntiay, the records of Ii, wi bc-acccsscd in the order of physica address, resuting in far fewer bock accesses. Thus, the partia-operation cost for II, (note that the cost of accessing R, records as owners through a SET is incuded in the partia-operation cost for the mcmbcr record type RJ is dcpcndent on the access structure of R, (i.e., depends on whether or not R, is stored scqucntiay), which vioates the condition for separabiity. c Situation 2: Figure 4-2 describes four record types, R,, R,, R, and R,. Set types S,, S,, and S, are dcfincd among them. If the pacement of R, records is decared as CLUSTERED VIA SEX S, NEAR OWNER, then R, records wi be custered. around R, records. Simiary, if the pacement of R, records is decared as CLUSTERED VIA SET S, NEAR OWNER, then R, records wi be custered around R, records. Let us assume that the pacement strategy of R, records is CLUSTERED VIA SET S,. Then the accessing of the member records (R. records) of an occurrence of SET S, wi be different, dependmg on whether R2 or R, is custered via its SET (S2 or S,) near the owner R,, since the intervening records wi affect the distances between R, records. Thus, the partia-operation cost for R, is dependent on the access configurations of R, or R,, which vioates the condiiion for separabiity RoI I 3 * RI I / \ % + S Rz I I IR3 Hgurc 4-2: Record Types R,,R,,R,,R3 with SET Types S,,S,,S3 In the mode introduced in this section, a significant portion of the access structures provided by the CODASYL 78 Database Specification is incuded. Those access structures excuded wi be incorporated by a heuristic extension Usage Specification The probem of designing an optima physica database for network mode systems is difficut because of the intrinsic procedura ccmcnts in those systems. Thus, once a physica database is designed according to a certain usage specification in a procedura form, thcrc is a possibiity that the usage pattcm wi I change as users pcrccive a new physica structure. This happens bccausc the usage specification in a procedura form dots not necessariy reprcscnt the optima transation of the nonprocedura specification. Nor can WC get the optima transation before WC have the specific physica database syructurc. (This is the cassic chicken-and-egg probem.) Athough the cyce may converge to some oca optimum, the true optimum cannot be achieved. Another difficuty with procedura specific&ions stems from data dcpendcncies. As an cxampc, et,us assume that a record key G defined in the conceptua schema and the subschcma and that the programs use it expicity. This key cannot then bc eiminated without changing a the programs that use it. Simiary, once a singuar set is defined in the schema and used by programs, it cannot be eiminated without changing these programs. In the system described by the DBTG proposa [COD 711, once a CALC kqy has been defined and used in appication programs, it cannot be redefined without jeopardizing those programs. One possibe approach to averting a these probems woud be to empoy a nonprocedura usage spccitication. We woud then have to have a hypothetica optimizer to transate the transaction in a nonprocedura form into an optima sequence of operations. In principe, the design can be accompished as foows: Enumerate a possibe access configurations of the physica database Using the hypothetica ojtimizer, evauate the minimum possibe processing cost for each configuration Find out the access configuration that yieds the minimum cost. If we design the optima physica database structure, initiay. based on a nonprocedura usage specification, the appication programs wi adapt themseves towards the true optimum. A good initia design is particuary important when a fu data independence is not provided by the system. We choose here a scheme for the usage specification that is rather nonprocedura and is simiar to the approach used in [GER 771. The usage is divided into 2 casses: one is the usage representing the entry to the database, the other the traversa of SETS, in which a the interactions among the different record types arc refected For the SET traversa, the directions of the traversa (i.e., owner to member or member to owner) are expicity specified in the usage. On the other hand, a the processing for the database entry is subject to optimization. Thus, for each operation, a decision has to be made as to which key is to be used (if the operation has a predicate that matches more than one key), whether a scan using the record-order key or the singuar set is to bc pcrformcd, ck., SO a~ to yied the minimum cost. The fixed direction of a ShT traversa is necessary to make the design- separabtc, since, otherwise, both directions have to bc considered, and the choice of the direction wi depend on the access configurations of both record types. The two casses of usage information are as foows: Proceedings of the Eighth Internationa 101 Mexico City, September, 1982

5 For database entry resoved before the record is fetched. of,,, (T, R, PRft D) is the frcqucncy of entry to the record type II in processing the transaction T. PRED rcprcscnts the predicate. which is in the conjunctive norma form, to be appied to the record type R. A s&q& predicate is an equaity predicate on one data item, such as DATAITEM = DATAVALUE. A candidate key is defined as the ist of a data items, each of which appears in a conjunct of PRED that is a simpe predicate. Ony candidate keys are considcrcd as potentia record keys to be supported in the storage schema. For SET traversa of,, (T, R, S, PRLCD) is the frequency of traversa of SET type S, in processing transaction T, from the owner to the member (record type R). PRED is the predicate to be appied to the owner record type. o &, (T, R. S, PRED) is the frequency of traversa of SET type S, in processing transaction T, from the member (record type R) to the owner. PRED is the predicate to be appied to the member record type. These parameters arc iustrated in Figure 4-3. fo,(t,r2,s.pred($)) ---- > ----_ R, j ----?J 1 R, I I I <---- f,,(t,r2,s.pred(r,)) Figure 4-3: Usage Parameters for SET Traversa CsW\.&R, area-scan) The cost of scanning the records of type R by scanning the whoe arca. Co,(Rt 9 CMoR 9 The cost of traversing one SET occurrence of type S from the owner record to its member records (of type I{). The cost of accessing the owner record is excuded since the owner record must have been acccsscd through other access structures that beong to the owner record type. The cost of accessing mcmbcr records and the owner record when traversing one SET occurrence of type S from a member record (of type R) to its owner. The starting member record is assumed to have been accessed aready. Usage-Transformation Functions In Section 4.3, the usage associated with SETS was specified as the frcqucncies of traversas of SET types. This must be transated into the fiequencics of traversas of SET occurrences. WC need the foowing definition and notation: (The usage transformation scheme that wi be described here is suitabe for the queries of two record types. The usage specification for the queries of more-thantwo record types is currenty being deveoped. It mainy has to dea with predicate branches in the query graph.) Definition 4: The inkage ficmr J,, of a record type R with respect to a SET type S is the ratio of the number of records of type R that are inked in any occurrence of S to the tota number of records of type R. (This is simiar in concept to the join seectivity in reationa systems VHA-a 811.) C. Number of records of record type R (cardinaity) Formuation of Partia-Operation Costs To formuate the partia-operation cost, we deveop the foowing notation. Ehncnbry-Operation C&R, Costs PRED, candidate-key) The cost of scanning the records of type R using the candidate-key with predicate PRED. C&&R, singuar-set) The cost of scanning the records of type R using a singuar set. CSCI\$, record-order-key) The cost of scanning the records of typ;c R using the record-order-key. The prcdicatc is not grls owner(r,s) SEL(PRED,R) : Number of member records (of type R) in a SET occurrence of SET type S (grouping factor). : The owner record type of SET type S whose mcmbcr record type is R. : Seectivity of predicate PRED when appied to the records of type R. WC now define three usage-transformation functions in accordance with three SET-reated usage parameters. Fo,(foM, T, R, S, PRED)= fom(t, R, S, PRED) X (1) n o,,,ner(rs) X SEUPRW ownerw9) k Jowner(asXs FMo(f,,, T, R, S, PRED)= fm,(t, R, S, PRED) X b((n, X J,,,)/gR,s, gk,s, n,, X SEL(PRRD, R)) (2) Proceedings of the Eighth Internationa 102 Mexico City, September, 1982

6 Hcrc the function b(n1.g.k) computes the number of record groups sccctcd. whcrc k is the number of records sccctcd, g the number of records in a group, and m the toti number of record groups considered. In ths form in Equation 2, the b function gives the number of.set occurrcnccs that have at east one mcmbcr record (of type R) satisfying prcdicatc PRED. An exact form of this function and various. approximation formuas arc summarized in [WHA-b 811. It is approximatey inear in k when k<<n (n=mxg), and approaches m as k bccomcs arger. A f&iar approximation suggcstcd by Cardenas [CA I< 751 is b(m,g,k) = m [ - (1 - /g)k]. I arti:-operation Cost Given an access configuration of the physica database, the paria.opcration cost of transaction T for record type R wi be whcrc and Cos~,,,,,,,<,( L N = x min ( PRED Cost S:T-TwLxSE(7 R, = z xc (9 SE{WT types whose member is R) PRED Fo,(f,,, T, R, S, I RED) X CJR, S) + FMO( fm,, T, R, S, PRED) X C&R, S)}. Entries in Equation 4 marked with the symbo 7 are considered ony when the corresponding access structures (singuar set or record-order key) are avaiabe in the given access configuradon Separabiity for the Mode System To verify that the design of the physica database for our mode is indeed scparabc, WC have to show that the partia-operation cost POC(T,R) for record type R is indcpcndcnt of the acces structures chosen for the other record types. For this purpose, we sha consider each individua component of the partia-operation cost. First, as shown in Equations 1 and 2, the usage-transformation functions arc ihdcpcndcnt of acces structures. They dcpcnd soey on the characteristics of the data such as the cardinaity of a record type, inkage factors, grouping factors, or the sccctivity of a prcdicatc for a record type, etc. (Thcsc arc aready known at design time.) 1 icincntar)i-opcr;ition costs C,,N, and C Y(,hU for a record type, say R. NC not :i iilctcd by the accc s structtirci of record types other th:r I:. WC ri ; ;on as foows: 0 I :ntcring the d~abasc through record type R ncccsscs ony records of type 11. e The records to bc actuay acccsscd and the order of accessing them arc dotcrmincd by the characteristics of the access structures of R itsef. o In accordance wirh our assumption in Section 3, custering of mcmbcr records (but not near owner), access structures such as indexes, or various SIY impcmcntations in any record type other than R, do not affect the rcaive distances of records of type R. o The accessing cost when using a CA1.C key is not affcctcd by any acces structures, since, on the basis of our assumption in Section 3, this wi dcpcnd soey on the oad factor of the area. Co,(R, S), the cost of accessing the mcmbcr records (of type II) of one SET occurrcncc when it is travcrscd from the owner to mcmbcrs, is dcpcndent ony on the access structures (e.g. SE1 impcmcntation or custering) of R itsef, because of reasons simiar to those above. C,,(R, S), which is the cost of accessing mcmbcr records and the owner record of one SET occurrcncc when it is traversed from a mcmbcr to the owner, consists of two components: the cost of accessing the member records and the cost of accessing the owner record. The former can be cxpaincd as in die previous cast (CoM). I hc atter dcpcnds on whether the records of type Ii (which is the member) arc custered on the inking data items. If so, the same SET occurrence and accordingy the same owner record wi be acccsscd consccutivcy. The owner record may we stay in the buffer and cause one bock access for one set occurrence. Howcvcr, if the mcmbcr records are not custered, a SET occurrence can be traversed repcatcdy in a random order (i.c., not consccutivcy) and v:i cause one bock access to access the same owner record for each traversa of the SET occurrcncc. Thus, the cost of accessing the owner records through a SET is dcpcndcnt on the acces structures for its mcmbcr record type. This is why WC incuded that cost in the partia operation cost for the mcmbcr record type. I,ct us note that this cost dots not dcpcnd on the acces structures of the owner type. Since a the components of the partia processing cost for record type R are indepcndcnt of the access structures of other record types, so is the partia processing cost, thus satisfying Condition 1 for separabiity. Condition 2 in Thcorcm 1 is satisfied, since WC arc not rcstrictcd at a in our choice of ccmcntary operations (for database entering or SET traversing) for a record type by choices made for other record types. (This condition may bc a significant restriction upon reationa systems, cspcciay in the sccction ofjoin agorithms.) Proceedings of the Eighth Internationa 103 Mexico City, September, 1982

7 Hcncc, WC concude that entire design proccdurc for our mode system is scparabc Exampe Cost Mode As an exampe, et us investigate the cost mode deveoped by Gcrritscn [GER 771. Based on a simiar system [GER 761 described in the DM G proposa [COD 711, it is,prcsented here,in a sighty moditicd form incorporating the foowing assumptions to be consistent with the assumptions WC have used: xrs Zit B LF %s o Member records of a SET occurrence cannot be custered near their owner. A the records of any type are stored in one area. The difference between sequentia and random bock accesses is ignored, so that the cost measure is simpy the number of bock acccsscs. Predicates are normay assumed to quaify more than one record, so that a the records of a type have to be accessed when they are scanned. (If it is known that ony one record satisfies the predicate, ony about haf the records; on the average, wi have to be accessed, which is the ony case considered in [GER 771.) The foowing notation wi be used in the cost mode: 1 if the pacement strategy of record type R is CLUSTERED VIA SET S, and 0 otherwise. Size in bytes of a record of type R. Size in bytes of a bock. Load factor of the arca in which the database is stored. Here it is assumed to be constant throughout the design procedure. Number of records of type R- (which is the member) in a SET occurrence of type S. QS 1 if SET type S has the owner pointer, and 0 otherwise. k P f Number of records of type R (cardinaity). Number of bocks in the area. An overfow function indicating the average number of bock acccsscs, in excess of 1, required to retrieve a record by a CALC key. WC define MAC(R, S) (mcmbcr-accessing Cost) as the cxpccted cost of competing the physica accesses rcquircd to visit a the members (of type R) of an occurrcncc of SET type S. Then we have MAC(R,S) = xrsx [(ZRXgKS)II(DX( C - XR,J x EC&,: - O.SLF))+ The first term cacuates the average number of bocks touched when the paccmcnt strategy for record type Ii is CLUSTERED VIA SET S. The factor 0.5 in the d enominator is for adjusting the oad factor. This factor is obtained based on the assumption that the oad factor is 0 when the first SET occurrcncc is oaded, whereas it is LF when the ast SET occurrence is oaded. The second term rcprescnts the cost when the pacement strategy of the record type R is not CLUSTERED VIA SET S, in which case the records in a SET occurrence arc accessed randomy. Using MAC&S), as foows: we can obtain the eementary-operation costs C&R, Cac-key) = 1 + f(lf) (6) C,,(R, singuar-set) = nr CJR, S) = MAC(R, S) C,,(R, S) = (-Q,) X 0.5 X.MAC(R, S) + 1 In Equation 9, it was assumed that accessing the owner record causes one bock access for each traversa of a SET occurrence regardess of whether a SET occurrence is traversed consecutivey or randomy. We note that a the eementary costs in this mode for record type R are independent of access configurations for the other record types; consequenty, the design is separabe Update Cost Athough a detaied usage specification for update transactions wi not bc dcvcopcd here, the foowing points arc worth noting. An update operation can be viewed as a series of operations that ocate the record to be updated as we as those that arc accessed on the way of ocating it. Thus, usage specifications simiar to the ones used in previous sections can bc empoyed for the updates. As mentioned previousy, WC incuded the cost of accessing the owner record through a SET in the partia-operation cost of the member record type. By the same token, the cost of updating the pointers (used for a specific SE Impementation) of the records of the owner record type of a SET must be incuded in the partiaoperation cost of the mcmbcr record type. This is bccausc the cost is a function of the specific SI:: impcmcntation, and the SKr impcmcntntion is rcgardcd as an access structure of thc mcmbcr 6,!8) (9) Proceedings of the Eighth Internationa 104 Mexico City, September, 1982

8 record type. It is not difficut to concude that, if we scgrcgate the costs into partia-operation costs for each record type as dcfincd in Section 4, update costs for a record type other than that of SET pointers w i not be affected by the access configurations for the other record tyk 5. Design Agorithm In this section, an agorithm for the design of optima access configurations wi be presented. Based on the resut of Theorem 1, the agorithm is as foows: Inputs: Usage information: f,,,, fo,, f,, as defined in Section 4.3, for each transaction, record type, SET type, and predicate, together with their respective frequencies. Usage specification of update transactions with their frequencies. Data characteristics: for each record type-its cardinaity, the size of a record, seectivity of the domain of each data item, the grouping and inkage factors of a record type with respect to the SET types connected to it. The conceptua schema specifying SET types defined among record types, SET seection strategy, etc. Agorithm: 1. Using the given usage information and data charactcri:tics, evauate the usage-transformation functions (F,,, F& for every transaction, record type, SKY type, and predicate. 2. Pick one record.type and determine the optima access configuration as foows: a. Pick one possibe access configuration of the record type. b. Given that access configuration, identify the best processing method for each eementary operation (corresponding to an eementary-operation cost) and cacuate its cost. c. Cacuate the partia-operation cost of each transaction. This is done by summing up a the eementary costs identified in Step b-mutipied by their respective frequencies-and a the costs incurred by the update transactions acting upon this record type. d. Repcat Steps b and c for a possibe access configurations for the record type under consideration. Then determine the one that gives the miniina cost as the optima configuration for that record type. aggregate resut for a record types constitutcss he goba optimum. The designer coud perform Step 2 in the Design Agorithm by the designer by trying each access configuration with a tria-anderror method. This is simiar to the approach used in [GAM 771, except that now WC are considering ony one record type ht a time. Since there are many different access structures to be chosen, however, even for one record type, enumeration of a the possibe access, configurations coud be an extensive procedure. An aternative approach is to partition the singe record type design into severa substcps, using heuristics if necessary, with w&defined interfaces. As excmpificd in [WHA-a 811 for a reationa system, tic design procedure coud be partitioned into the foowing two substeps: Determination of the pacement strategy (this corresponds to custering in reationa systems) such as CALC and CLUSTERED VIA set-name, where set-name stands for any SET type whose member is the record type under consideration. Seection of auxiiary access structures such as indexes, singuar sets, and the record-order key. This approach shoud be expored in more detai in the future. 6. Extensions for the Other Access Structures An extension of the access structures not incuded in the basic design methodoogy, such as SEQUENTIAL and CLUSTFXED VIA SET NEAR OWNER, can be accompished by using heuristic methods. After the basic design is obtained by using the Design Agorithm in Section 5, the SEQUENTIAL option can be considered for each record type (ony one at a time is endowed with this property). The tota costs with or without this option are compared and the differences cacuated for each record type. (Since the SEQUENTIAL structure may affect the partia-operation cost for other record types, the tota processing cost has to be considered for comparison.) Record types must be ranked in importance according to the cost differences. The record type that yieds the greatest benctit is assigned the top rank. The pacement strategy is then actuay changed to SEQUENTIAL-if the tota cost is reduced- starting with the top-ranked record type. Another approach for the SEQUENTIAL option is to incude it in the basic design methodoogy, pretending that the design is separabe and sacrificing sighty the rigorousness of the property of separabiity. The major prospects for this option wi be record types that require frequent scanning of a their records. But this type of operation does not impair separabiity, so that we can keep the error minima whie pretending that the design is separabe. 3. Step 2 is repeated for cvcry record type in the database. The The CLUSTERED VIA SET NEAR OWNER option can be Proceedings of the Eighth Internationa 105 Mexico City, September, 1982

9 consitcrcd next. For cvcry record type whose puccmcnt strategy is C.~Js I IXIII) VIA SyI, rhc atter is changed temporariy to C.USI Xi) VIA S: N A OWNIIR (ony one record type at a time is cndowct wih this propcrly) and titfcrcncc in totn cost is cacu~tct. As in t~\: cast of SI~QUI~N I A. option, the importance of the record types is ranked. hc paccmcnt stt%tcgy is then actuay changed :o C.US E~E) VIA SE 1 NEAR OWNER-if thcrc is a cost benefit-starting from the top according to the rank. Constraints can bc used hcrc, if dcsircd, that not more than one mcmbcr record type can bc custered near the same owner record type. this approach is simiar to the one in [KA I X0] but uses a more quantitative approach to estabish the rank. Marc rcscarch needs to bc done on usage specifications for update transactions and on the design agorithm for a singe record type. Now that the whoe design has been partitioned to the designs of individua record types, any conventiona method devised for a singe ogica object can bc appied hcrc. 7. Concusion A physica design methodoogy for network mode databases has been introduced. Our main objective in this method is to estabish a forma design methodoogy, based on the idea of separabiity, in which a arge subset of practicay important access structures are incuded. fhcn, using heuristic methods, WC proceed to cxtcnd this basic design to incude other XCESS structures that have not been incorporated initiay. hc CODASY I, 78 Database Spccitication has been used as our environment for our discussion. WC have introduced a usage specification scheme that is suitabe for describing the network mode database environment. It has been proved that, under this schcmc, the secctcd set of access structures indeed satisfies the conditions for separabiity. It has been cmphasizcd that the initia design is cspcciay important in the systems that do not provide a fi1 data indcpcndcncc. Our approach provides a too to achicvc the optima initia &sign LSiig a argey nonprocedura usage specification. In sum:nary, die key contribution intcndcd in this paper is to provide a forma methodoogy for the physica design of network mode databases. Refe races [IM I 801 [CAR 751 [COD 711 3atory, I>. S. and Goticb. C. C., A Unifying h4odc of Physica Databases, Tech. report CSRG- 109, Computer Systems Rcscarch Group, University of Toronto, Apri Cardcnas, A. F., Anaysis and P&ormancc of Inverted Database Structures, c otwn. nc /\i, Vo. 18, No. 5, May 1975, pp CODASYI,, Dar 1 Base 7 ask Group Iepor, ACM, New York, [COD-a 78]CODASYL Data Description.an~uagc Cotnmittce, Journa of Devehpmrrr. EIIP Standards Committee, Sccrctariat of Canadian Govcrnmcnt, Canada, [COD-b 781 CO)ASY, Cobo Comtnittce, Journa of Devevpmen~, EDP Standard Committee, Sccrctariat of Canadian Govcrnmcnt, Canada, [CAM 771 [GER 761 [Ci :ir 771 [t ;\M 761 [I-I!3 701 Gambino, T. J. and Gerritsen, R., A Database Design Decision Support System, hoc. td. Cor$ on Very Z.arge Dafabases. Tokyo, Japan, IEEE, October 1977, pp. 534-w. Gcrritsen, R. et a., WAND User s Guide, Decision Sciences Working Paper , Wharton Schoo, Univ. of Pennsyvania, Gcrritscn, R. et a., Cost Effective Databsc Design: An Integrated Mode, Decision Scicnccs Woiking Paper Wharton Schoo, Univ. of Pennsyvania, ammcr, M. and Chan, A., Index Sccction in ;I Scf- Adaptive Databnsc Managcmeut System, hoc. It& C otf: O/I Maunagernor~ of Dafa, Washington, D.C., ACM SLGMOD, June 1976, pp Hsiao, D. and Harary, F., A Forma System for Information Rctricva from Fies, C orrrm. Ac nf, Vo. 13, No. 4, February 1970, pp , Aso xc Comm. ACM 13.4, Apri 1070, p.266. Acknowedgment r his work was supported by the Dcfcncc Advanced Research Projects Agency, under the KBMS project, Contract Number N39-82-C I hc authors wish to thank the rcfcrccs for their usefu commcats which made the fina version more comprchcnsive. [KAT 801 [SCH 751 [SCH 791 Katz, 1~. F-. and Wong, B., An Access Path Mode for Physica Database IIcsign, Proc. td. Conf: ON hatrczgetrwtrf of Dtrm, Santa Monica, Caif., ACM SIGMOD, May 1980, pp Schkonick, M., 1%~ Optima Sccction of Secondary Indices for Fies, It$mra/iotr SJWMIIS, Vo. 1, March 1975, pp. r-146. Schkonick, M. and Tibcrio, P., Considerations iti Dcvcoping a I)csign Foo for a Ikiitiona DBMS. Cott~pwc, nov 1979, pp Proceedings of the Eighth Internationa 106 Mexico City, September, 1982

10 (S!iV 751 Scvcrancc, I). G., A I ~ iwtk Mode of htcrnative Fie Structures, Ir~&mr~io~~ Sjwwr,~ \ o. 1, No. 2, 1975,pp [WM-a 811 Whdng, K., Wicdcrhod, G., and Sagnowicz, D., Separabiity: An Approach to Physic;+) Database Design, Proc. td. Cotrf: ott Very I,qrge DaabaseK Cannes, Frnncc, IEEE, Sqtcmbcr 1981, pp PVIIA-b 811 Whang, K., Wiedcrhod, G., Sagaowicz, D., Estimating Bock Accesses in Database Organi7,ations- A Cosed Noniterativc Formua,, submitted for pubication, [WIE 771 Wicdcrhod, G., Dtrtahase Design, McGraw-Hi Book Company, New York, WA0 771 Yao, S. B., An Attribute Based Mode for Database Access Cost Anaysis, ACh Trans. Dntabnse Sysems Vo. 2, No. 1, March 1977, pp Proceedings of the Eighth Internationa 107 Mexico City, September, 1982