DATA STRUCTURE DIAGRAMS

Transcription

1 DATA STRUCTURE DAGRAMS By Charles W. Bachman Successful communcaton of deas has been and wll contnue to be a lmtng factor n man's endeavors to survve and to better hs lfe. The nventon of algebra, essentally a graphc technque for communcatng truths wth respect to classes of arthmetc statements, broke the bond that slowed the development of mathematcs. Whereas "12+ 13=25 '' and "3+7= 10" and "14+(-2) = 12" are arthmetc statements, "a+b=c '' s an algebrac statement. n partcular, t s an algebrac statement controllng an entre class of arthmetc statements such as those lsted. Data Structure Dagrams The Data Structure Dagram s also a graphc technque. t s based on a type of notaton dealng wth classes--specfcally, wth classes of enttes and the classes of sets that relate them. For example, ndvdual people and automobles are enttes. When they are taken collectvely, they make two qute dfferent classes of enttes. On the other hand, all the automobles belongng to a partcular person consttute a set of enttes that are subordnate to the owner entty. The Data Structure Dagram has been used frutfully over a perod of fve years by a lmted but rapdly growng audence. Ths audence (where the technque orgnated) conssts of the users of General Electrc's ntegrated Data Store (-D-S) data management system. -D-S employs language statements that drectly support the relatonshps mpled by the Data Structure Dagrams. The technque s now beng used to study, document, and communcate nformaton structures, even n those cases where no mechanzed mplementaton s ntended. The purpose of ths paper s to document the technque of data structure dagrammng so that t may be studed, evaluated, and put to work where t appears useful. Defntons Four terms: entty, entty class, entty set, and set class are central to the understandng of Data Structure Dagrams. Ths text wll use the term entty to mean a partcular object beng consdered; the term entty class wll mean an entre group of enttes whch are suffcently smlar, n terms of the attrbutes that descrbe them, to be consdered collectvely. Many dfferent entty classes may exst. The text wll use the term entty set to mean a dfferent knd of CHARLES W. BACHMAN s Manager, Applcatons Technology, for Genera/ Electrc, Phoenx, Arzona. He s the creator of G.E.'s ntegrated Data Store (-D-S), a generalzed data storage and retreval system. He s also a member of the COBOL Data Base Task Force. entty groupng--one that assocates a group of enttes of one entty class wth one entty of a dfferent entty class n a subordnate relatonshp. The concepts of entty class and entty set are ndependent of each other and can be thought of as beng at rght angles or orthogonal. Fgure 1 llustrates ~hs pont. entty set entty Fgure 1 entty class The term set class wll be used n the text to mean an entre group of entty sets whch are suffcently smlar, n terms of the attrbutes that descrbe them, to be consdered collectvely. Specfcally, t s lmted to those groups of sets n whch the same entty-to-entty subordnate relatonshp exsts. Fgure 2 expands on Fgure 1 to put all four of these terms nto a spatal relatonshp. entty set set class entty Fgure 2 entty class Many dfferent set classes may exst. For example, the enttes that we mght consder n a management nformaton system are the employees and the departments. All the employees n the company, when consdered together, would make one entty class, whle all the departments would make another entty class. Although the departments and employees may be consdered ndependently of each other for some purposes, the relatonshp between the group of employees who work for the same department and that department may also be very mportant. nsofar as a department has a set of employees currently assgned to t, these employees can legtmately be consdered as subordnate enttes or sub-enttes of that department. Each department s consdered to be the owner of the set n whch.ts employees are the members. When all of these 4

2 sets of employees are consdered collectvely they consttute a set class. n a lke manner, f employees, as an entty class, were consdered n conjuncton wth ther spouses and chldren, whch comprse yet another entty class, then a set class could be establshed on the bass of the sets wth employee enttes as owners and ther spouse and chldren as members. The concept of owner and member, the one owner to many member rato, and the fact that these may be treated on a class bass, are central to the purpose and graphcs of the Data Structure Dagram. Graphc Symbols The Data Structure Dagram technque uses two basc graphc symbols: the block, to represent an entty class; and the arrow, to represent a set class and to desgnate the roles of owner/member establshed by that set class. The arrow ponts from the entty class that owns the sets to the entty class that makes up the membershp of the sets. The dagram n Fgure 3 states that an entty class exsts and that an entty class name s to be assgned. No nformaton s mpled as to how many enttes make up the entty class. The only mplcaton s that the entty class has been declared and s subject to such operatons as may be defned. were beng studed, there would be as many department enttes and employee enttes as that company had departments and people. The dagram n Fgure 5 states not only that two entty classes exst, but also that they are related by a set class named "assgnment." The drecton of the arrow s read to mean that each employee s a member of a set of employees that belong to a partcular department, and further, that each department has such a set of employees. SET ASSOCATON OF ENTTES department owner ~assgnment Fgure 5 employee member CLASS OF ENTTES entty-class-name J The Data Structure Dagram s topologcal n nature. Only the blocks, arrows, and names have meanng. The ~ze, poston, and proporton are selected for readablty. Fgure 6 s exactly equvalent to Fgure 5, even f somewhat contorted. Fgure 3 TOPOLOGCAL GRAPHCS The dagram n Fgure 4 states that two entty classes have been defned and that ther entty class names are: "department" and "employee." f a partcular company TWO CLASSES OF ENTTES department Fgure 4 employee ] rlguru A Data Structure Dagram may contan as many blocks and arrows as necessary to establsh the partcular nformaton structures under study. Any two entty classes may be assocated as entty class/sub-entty class by zero, one, two, or more dfferent set classes wth the same or opposte ownershp. o

3 Herarches The term herarchy has been used rather ambguously n the feld of nformaton technology. Data Structure Dagrams provde one possblty for non-ambguous defnton,.e., an nformaton herarchy can be sad to exst wherever there s a set-class relatonshp. Therefore, an nformaton herarchy exsts whenever there are two or more levels of assocated entty classes. Fgure 7 ntegrates the department/employee assocaton of Fgure 5 wth the employee/ dependent assocaton mentoned earler to provde an ex- The Data Structure Dagram that defnes a network s seen n Fgure 9. SMPLE NETWORK STRUCTURE ample of a three-level herarchy, domnant dependent node HERARCHY! ' [relatonshp department Fgure 9 ~ assgnment The two entty classes labeled "node" and "relatonshp" relate to the nodes and lnes between nodes n Fgure 8. employee! By settng up a table of equvalences (Table 1), several dfferent models whch are network-orented can be quckly defned. Please do not confuse the arrow drecton n the ~ famly network (Fgure 8)--meanng the domnance of one node over another wth the arrow drecton n the network Data Structure Dagram (Fgure 9) meanng an owner/member role. dependent Fgure 7 Many actual structures can be modeled ether as a herarchy, network or tree. When the elements n a real world herarchy are lke enttes (.e.,all people, all organzatons) and ther reportng level s subject to change, then a network or tree structure may prove to be more satsfactory n modelng the stuaton than a herarchcal structure. Networks Many nformaton models nvolve networks of nformaton, PERT or CPM dagrams are examples of such networks. Another example s the "T" account double-entry accountng system n whch every entry affects the debt sde of one account and the credt sde of another account. Fgure 8 s a generalzed pcture of a network wth nodes connected to each other n a drected sense, or as a drected graph. NETWORK Fgure 8 6 PERT/CPM APPLCATON GENERAL ACCOUNTNG PARTS LSTS GENEALOGCAL CHARTS Event ENTTY CLASS NAME NODE Account Materal terr Subject SUBROUTNE STRUCTURE Subroutne ORGANZATON CHARTS Organzaton SET CLASS NAME RELATONSHP DOMNANT DEPENDENT Table 1 Actvty Pror Succeedng Transacton Debt Credt Component Call-Out Where Used Relatonshp Parent Chtd Call Enter Return Component Sub-Unt Report-To The smlarty of the PERT/CPM dagrams to a network s obvous. That of the general accountng model may be less obvous. But what are the transactons, except drected quanttatve relatonshps between accounts (nodes); the tral balance should always be zero. Manufacturng parts lsts conssts of materal tems, whch are made out of materal tems. Genealogcal charts are smlar to manufacturng parts lsts except that each tem s made from only two other thngs, ts parents. The nterrelatonshp of a set of subroutnes that call on each other s also a network because each subroutne may call many subroutnes or be called by many subroutnes. Tree Structures Organzaton charts usually are specal cases of a network, the tree structure, n whch each node has one

4 dependent relatonshp and many domnant relatonshps. say usually, because mltary organzatons are rfe wth stuatons where unts are assgned one place for command purposes and another for ratons and quarters. Fgure 10 llustrates a tree structure. TREE Fgure 10 The Data Structure Dagram n Fgure 9 s equally good for modelng a network or a tree. The Data Structure Dagram n Fgure 11 s more specalzed n that t supports a tree model but does not support a network. domnant TREE STRUCTURE node ~L relatonshp Fgure 11 dependent n the Tree Structure Dagram the owner/member relatonshp (arrow) of the "dependent" set class has been reversed. The freedom to make the reversal s based upon the fact that the tree allows only one or no relatonshps on the dependent sde of the node. Modellng the tree wth a Data Structure Dagram permts two optons: (1) one relatonshp entty ownng a one-member set of node enttes (Fgure 11), or (2)one node entty ownng a one-member set of relatonshp enttes (Fgure 9). Therefore, the drecton of the entty/sub-entty relatonshp s somewhat arbtrary. From the Data Structure Dagram n Fgure 11, t s a short step n structure smplfcaton to reach the dagram n Fgure 12, whch stll represents the tree. TREE STRUCTURE DAGRAM node U domnant Fgure 12 The "dependent" set had been lmted by defnton of a tree to a 1:1 relatonshp between the "node" and "relatonshp" enttes. Ths was the fact whch permtted reversng the dependent entty/sub-entty assocaton n Fgure 11 and stll further supported mergng the "node" entty class wth the "relatonshp" entty class. The dagram smply llustrates that each "node" has a "domnant" relatonshp wth other nodes that, n turn, are lmted to one relatonshp on what s consdered ther "dependent" sde. The Data Structure Dagrams n Fgures 11 and 12 create a chcken and egg stuaton. A member entty cannot exst untl there s a set n whch to nsert t. n Fgures 11 and 12 the "node" entty s both owner and member. Therefore, one such entty cannot exst alone unless t s ts own owner. Two dfferent structure solutons are avalable for ths dlemma. These are the sometme member entty classes, descrbed n the next secton, and the alternate owner set classes, whch wll be dscussed later n the text. Sometme Member Entty Classes When t s necessary to document a set class n whch the member relatonshp may or may not exst, a dashed arrow s used. Fgure 13 llustrates the graphc conventon. Enttes of the owner entty class always own a set of the set class specfed. Enttes of the class at the head of the arrow n Fgure 13 ndvdually may (or may not) be members. SOMETME MEMBERSHP owner 1 T Fgure 13

5 An example of a sometme member can be drawn from the bankng ndustry, where demand depost accounts enttes have a sometme relatonshp wth an overdrawn account entty. Whenever an account's balance s less than zero, the relatonshp s nvoked untl pad up. Otherwse, the relatonshp doesn't exst. Compound Networks We have just used some examples of smple networks to llustrate the usage of Data Structure Dagrams. By smple network, mean networks of lke enttes,.e., all events, or all "T" accounts. Compound networks are the result of the assocaton of unlke enttes wthn a network. One example of a compound network s developed by the author assocaton between books and the people who wrote them. f you were to examne the books n any lbrary, you would fnd that some books had one author whle other books, especally n the techncal and educatonal felds, had two and maybe three or four authors. f you consdered the people who were authors of these books, you would fnd that some were authors of more than one book. Certan prolfc authors would have many books to ther credt. Therefore, the network created by the book/people/author relatonshp would consst of nodes for books (book enttes), nodes for people (people enttes), and a relatonshp between a book entty and a person entty that records authorshp. Fgure 14 s the Data Structure Dagram whch represents ths compound network. COMPOUND NETWORK STRUCTURE authorshp! ers n person-author school 1 department..-" Fgure 15 Ths model ncludes a school/department/person organzaton-orented herarchy, the person/dependent personnel-orented herarchy and the person/authorshp/book compound (publsh-or-persh) network. Gven the necessary computer hardware and software, and access to any one entty n a specfc data base created accordng to ths Data Structure Dagram, then all other assocated enttes could be determned by movng through the sets. Both General Electrc's ntegrated Data Store (-D-S) and General Motors' Assocatve Programmng Language (APL) are software systems specfcally desgned and mplemented to encourage and support the constructon, mantenance, and use of data bases organzed around such complex structures. Multmember Set Classes When t s necessary to document a set class wth more than one class of enttes n the role of member, a multheaded arrow s used. Fgure 16 llustrates the graphc conventon. MULTMEMBER SET CLASSES Fgure 14 nformaton models of any complexty usually are compound networks n one or more ways. f our orgnal department/employee model had represented a unversty, then the "employee" entty mght have been the same entty class name as the "person" entty wth a new assocaton. Fgure 15 combnes the Data Structure Dagrams of Fgure 14 and one smlar to Fgure 7 to create a more comprehensve nformaton model. Fgure 16

6 An example of multmember set classes can be drawn from the bankng ndustry, where each customer may have several dfferent types of busness wth the bank. Dfferent entty classes are establshed for demand depost accounts, savngs accounts, loan accounts, and trust accounts. Fgure 17 llustrates ths data structure. Wth ths structure, each customer can have multple numbers of accounts of the same or dfferent types. ALTERNATE OWNER SET CLASSES J CUSTOMER 1 ACCOUNTS Fgure 17 The need to provde for multcustomer assocatons wth specfc accounts,.e., jont accounts, usually leads banks to work wth a stl:ucture that ncludes jont account enttes. Fgure 18 shows ths extenson. Wth ths data structure, each customer can have multple numbers of accounts, and each account has one prme customer. n addton, each account may have any number of addtonal jont account customers. Thus, agan a compound network s descrbed. CUSTOMER Fgure 19 A partcular set has only one owner. Each owner entty has ts own set, but the set class name and the member entty classes of ts set are the same regardless of whch entty s the owner. An example of alternate owner set classes can be drawn from the manufacturng ndustry, where a manufacturng order may be placed on the shop by an nternal organzaton, a dstrbutng organzaton, or a customer. For accountng and reportng purposes, dfferent entty classes are establshed for each type of organzaton because dfferent nformaton must be mantaned or because they may be nvolved n other and dfferent set classes. However, from the shop's pont of vew, they are the "customer" for an order regardless of ther other nature. Another example relates back to the Tree Structure Dagram n whch ntaton of the tree posed a problem. Fgure 20 s an alternate soluton. f the "domnant" set class had alternate owners (ether a prmary node entty that s owner but not member or a secondary node entry that s both owner and member), then the problem s trunk of the tree. The corollary of ths structure, f mposed on a data management system, s as follows, "f the prmary node were removed, then all of the secondary nodes and thus the entre tree goes wth t." TREE WTH TRUNK JONT ACCOUNTS Fgure 18 Alternate Owner Set Classes When t s necessary to document a set class wth potentally more than one class of enttes n the role of owner, a multtal arrow s used. Fgure 19 llustrates the graphc conventon. 9 Fgure 20 " ~

7 Complex Structures Very large Data Structures Dagrams have been desgned and used n the last fve years n the desgn and mplementaton of varous nformaton systems. "Large" n ths case s measured n terms of the number of entty classes and set classes. Fgure 21 llustrates the Data Structure Dagram underlyng one manufacturng nformaton and control system, MANUFACTURNG Fgure 21 STRUCTURE t has 39 entty classes and 38 set classes. Can you, n examnng the dagram, fnd a fve-level herarchy? Two smple networks? Fve compound networks? A smple network wth an extra herarchcal level n one leg? Note that there are no tree structures. Wthout any rgorous defnton, a complex structure s one composed of many entty classes and many set classes. Wthn a complex structure, we typcally fnd multlevel herarches, smple networks, compound networks and trees. Large Data Structure Dagrams, n terms of the number of elements, should be clearly dstngushed from large data bases wth many enttes (records), whch have been bult n response to a Data Structure Dagram. Although each entty n a data base needs an entty class to defne and control t, that one entty class may represent zero, one, ten thousand, or a mllon records n storage. The largest system n operaton today contans 60 entty classes controllng over half a mllon data records. Larger systems are beng nstalled. Summary of Structure Types Smple and compound networks are dfferentated by the fact that one, the smple network, s constructed of node enttes of a sngle entty class, whle the other s constructed of node enttes of several dfferent entty classes. Trees and networks are dfferentated by the fact that one, the tree, s constructed under the rule that each node has only one "domnant" node whle the other s constructed wth unlmted assocaton between nodes. The two concepts: tree vs. networks, and smple vs. compound, are ndependent of each other and can be thought of as beng at rght angles or orthogonal. Fgure 22 llustrates ths pont and brngs the herarchal structure nto perspectve. t s a compound tree,.e. wth more than one entty class as node and each node wth only one dependent assocaton. herarchy COMPOUND NETWORK tree ~ smple network only one ~ J~ only one dependent ~ J J entty class assocaton ~ ~ J as node per node entty Fgure 22 Summary The Data Structure Dagrams, consstng of two knds of elements (blocks representng entty classes and arrows representng set classes), have been defned. Examples have llustrated ther applcaton. Ther practcal usage n the desgn and study of mechanzed nformaton systems has been descrbed. Two data management languages, -D-S and APL, provde for the descrpton and manpulaton of data bases wth the characterstcs that are descrbable through the Data Structure Dagrams. n addton, there s a new Data Descrpton Language and Data Manpulaton Language currently beng specfed by the Data Base Task Group of the COBOL Programmng Languages Commttee. Ths offers promse for an ndustry standard data management language that would operate n conjuncton wth FORTRAN, ALGOL, PL/, as well as COBOL allowng a DATA BASE to be bult n one language whle beng accessed n yet another. Bblography (1) Bachman, C. W., Wllams, S. B., "A General Purpose Programmng System For Random Access Memores," Proceedngs of the Fall Jont Computer Conference, San Francsco, Calforna. October (2) Bachman, C. W., "Software For Random Access Processng" Datamaton, Aprl (3) "ntegrated Data Store, A New Concept n Data Management," AS-CPB-483A General Electrc nformaton Systems Group, Phoenx, Arzona. (4) Bachman, C. W., "ntegrated Data Store Data Base Study" Second Symposum on Computer-Centered Data Base Systems, also avalable as CPB-481A General Electrc nformaton System Group, Phoenx, Arzona. (5) Dodd, G. G., "APL--A Language for Assocatve Data Handlng n PL/," Fall Jont Computer Conference, (6) "Report to the CODASYL COBOL Commttee, January COBOL Extensons to Handle Data Base" prepared by Data Base Task Group. (7) "Data Descrpton Language and Data Manpulaton Language Report," Aprl 1969; Prepared as a report to the CODASYL COBOL Programmng Language Commttee by the Data Base Task Group. 10