# Margaret S. W% 425 Beldon Ave Iowa City, Iowa Phone: (319) ABSTRACT

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2 NORMALIZATION OF DATA To normalize a set of data items, we may proceed from frost normal form (lnf) to second normal form (2NF) to third normal form (3NF) to Boyce-Codd normal form (BCNF) to fourth normal form (4NF). In practice, we can proceed directly from lnf to BCNF. The use of BCNF rather than 3NF is preferred because normalization to BCNF is easily understood by students and can be quickly implemented, in addition, a relation in BCNF is dso in 3NF. To normalize a record type to lnf, any repeating fields or groups of fields are repeated for each record. The only attribute values permitted by lnf are single atomic values. A relation schema R is in Boyce-Codd normal form if whenever a functional dependericy X -> A holds in R, then there do not exist two tuples tl and t in R such that tl[x] = t2[x]. X is called a superkey o3 R. To define fourth normal form, the concept of multivalued dedendencv (MVD) is required. An MVD X ->-> Y holds for R(X,Y,Z) if and only if whenever (FY,Z) ad LY,z ) are tuples of R, then so are (Ly,z) and (XJ,Z ). An MVD X ->-> Y is said to be. trivial ify is a subset of X or XUY = R. follows: The deffition of 4NF is then given by Fagin [51 as A relation schema R* is in 4NF if, w~enever a nontrivial MVD X ->-> Y holds for R, then so does the functional. dependency X -> A for every column name of R. If X ->-> Y, we also say that Y is a mukivalued fact about X. It is possible for Y to be called a multivalued fact about X and yet the relationship between X and Y is not a mukivalued dependency. When a multivalued fact is not independent, i.e., a mukivalued dependency does not exist, redundancy of data values is necessary. To obtain 4NF, the relation R is decomposed into two or more relations which meets the constraints given by the deftition of 4NF. For the purpose of normrdizing real world data, we may restate the deftition of 4NF as follows: A relation R is in fourth normal form if R is in BCNF and does not contain any nontrivial multivalued dependencies. We note that this simpler statement does not conform fidly to the original deftition given by Fagin [4]. However, the theoretical differences do not affect the normalization of real world databases. Table 1 The nine databases with data violating 4NF Functional Total * Record Orszanization Area Fields Z!I&S Financial Firm Sales Management System Physician Database Data on Individual Physician 68 6 Publishing Firm Job Scheduling 63 9 ColIege of Nursing Student Skills Database 55 8 Apartment Complex Maintenance Tracking Division of Sponsored Grants Database 42 7 Research Animal Laboratory Inventory of Animals 33 5 Athletic Tutoring Program Assignment of Tutors 18 7 Automotive Parts Retailer Inventory

3 RESEARCH METHODS The databases from forty organizations were studied for this project. Each organization was a small firm, a division of a large fum, or a division of a major university. The database for each organization was limited to the data required for the functional area of the organization with the exception of one business firm which was studied in its entirety. Eighteen organizations were functional units within a large university, twenty were private firms, and the remaining two were government organizations. The study included the entire database for a reprographics firm, the manufacturing database for a Fortune 500 firm, and the sales management system for a major financial firm. These three large databases were examined for data that violated 4NF. The remainder of the organizations were studied by student teams for undergraduate classes in the Systems Analysis and Design course. Each team was required to present the data as a set of record types in 3NF. These reports were then carefully reviewed and revised by the author as necessary to obtain record types in 4NF. Additional contact with the organizations was made to resolve any ambiguities in the data and the relationships between the data. RESULTS OF THE STUDY This study has determined that data violating 4NF occurred at least once in nine organizational databases constituting over twenty percent of the databases in this study. Twenty of the 350 record types comprising the forty databases resulted from normalization of BCNF relations to 4NF. These record types represent six percent of the normalized record types in this study. Because of this incidence, 4NF is not so rare. Table 1 provides information regarding the data found in the organizational databases which contained data violating 4NF. The number of data fields for each organizational database has been tabulated. The number of normalized record types for each organization is also given. The tabulation of the number of data fields found at each organization yields a general picture of the magnitude of these databases. Both large and small databases were included in the study. The database represented by the 307 data fields required for the sales management system of a major financial firm was found to violate 4NF. The other eight databases contain an average of over 40 data fields. AVOIDANCE OF FOURTH NORMAL FORM It is sometimes possible to avoid the use of fourth normal form by representing the data differently. As an example of this approach, let us consider the database of the Financial Organization. This database in BCNF contains the following relation violating fourth normal form: Codes (ACCOUNT ID, HOME PENDING CODE, FIELD PENDING CODE) To obtain 4NF, thk relation is decomposed to form two relations: Home-Codes (ACCOUNT ID, HOME PENDI~U CODE) Pending-Reqts (ACCOUNT ID, FIELD PENDI~U REQUIREMENT) It is possible to represent the attributes of HOME PENDING CODE and FIELD PENDING REQUIREMENT so that the data does not violate 4NF. The value of these fields is given by a numeric value that indicates a particular item of information has not been received by the organization. For example, if the value of 01 is present for HOME PENDING CODE for a particular value of ACCOUNT ID, we know that the document identified as 01 has not been received. To represent this information without violating fourth normal form, we will require that all values for HOME PENDING CODE be given and an additional field called HOME-PENDING-CODE-Y-N be included. This latter field will contain either a Y or N value to indiciite whether a particular document identified by its corresponding value in the HOME PENDING COI)E field has been received or not. Similarly, we add the field P-REQTS-Y-N to contain a Y or N value corresponding to a particular value of FIELD PENDING REQUIREMENT. We then have two relations as shown below Home-Code-YN (ACCOUNT ID, HOME PENDING CODE, HOME-PENDING- CODE-Y-N) Pending-Reqts-YN (ACCOUNT ID, FIELD PENDING REQUIREMENT, P-REQTS- Y-N) These two relations do not violate fourth normal form and require no further normalization. Another representation for this data is possible by the use of buckets. In actuality, the HOME PENDING CODE field has only 19 possible codes while the FIELD PENDING REQUIREMENT field has only five possible codes. 21

4 Table 2 The Violations of Fourth Normal Form In this research study, nine databases were found to contain data violating fourth normal form. The relevant data for these nine organizations is shown below in relations normalized to 4NF. 1. Financial Organization - Sales Management System Home-ties (ACCOUNT ID, HOME PENDING CODE) Pending-Reqts (ACCOUNT ID, FIELD PENDING REQ UIREMEMP) 2. Physician Identification System Is-Member (PHYSICIAN ID, GROUP ID) Works-At (PHYSICIAN ID, LOCATION ID) 3. Publishing Firm - Scheduling System Associated-Job (JOB NUMBER ASSOCIATED JOB NUMBER) Colors (JOB NUMBERj COLOR REQUIRED) 4. College of Nursing - Student Skills Database Has-Prerequisite (SKILL CODE, PREREQUIWI E SKILL CODE) Course (COURSE, SKILL CODE) 5. Family Housing Office - Maintenance Tracking System Adjoining-Apt (AIT CODE, ADJOINfNG APT CODE) Maintenance (APT CODE, MAINTENANCE CODE, MAINTENANCE DATE) Spraying (APT CODE, SPRAY DATE, AREA SPRAYED) 6. Division of Sponsored Research - Grants Database Grant-Area (GRANT CODE, DISCIPLINE) Grant-Keyword (GRANT CODE, KEYWORD) Faculty-Interests (UNfVERSITY ID, KEYWORD) 7. Animal Laboratory - Inventory of Animals Account-Investigators (ACCOUNT NUMBER INVESTIGATOR NUMBER) Account-Animals (ACCOUNT NUMBER ANIMAL ID) 8. Athletic Tutoring System - Tutor Assignment Note: The Athletic Tutoring Service did not wish to classify individual courses by subject area(s) but did wish to track both courses and subject areas for which a student was deemed qualified to sewe as a tutor. Tutor-Subjects (TUT OR ID, SUBJECI_ AREA) Tutor-Courses (TUT OR ID, COURSE ld) 9. Automotive Parts Retailer - Inventory Vehicle-Engine-Part (W3 HICLE, MODEL. YEAR ENGINE TYPE, ENGINE FEATURE, ENGINE-PART-NUMBER) Vehicle-Feature (VEHICLE, MODEL, YEAR FEATURE, ~ Note: The field FEATURE consists of several subfields. 22

5 Consequently, we may choose to store thk same information in one relation as shown below All-Codes (ACCOUNT ID, HOME-PENDING- CODE-1,... HOME-PENDING-CODE-19, FIELD-PENDING-REQUIREMENT-1,... FIELD-PENDING-REQUIREMENT-5) Although the relation All-Codes is technically in 4NF, the use of the bucket violates the principles of the relational model. The organization may choose the bucket representation because these data fields have been in use for several years and it is unlikely that change would occur. The bucket representation presents potential problems due to its inflexibility. We note that the proper choice for data representation is dependent on the individual installation s preference for data representation, the requirements for flexibility, the need to minimize storage space, and the trade-off of data structure for ease of programming. 5. Fagin, Ronald. Multivalued Dependencies and a New Normal Form for Relational Databases+ ACM Transactions on Database Svstems, ~, 3, (Sept. 1977), Fife, Dennis, W. Terry Hardgrave, and Donald R. Deuth. Database Concepts. Cincinnati Southwestern Publishing Co., Kent, W. A Simple Guide to Five Normal Forms in Relational Data base Theory, Communications of the ACM, 26, 2, (Feb. 1983), Mittra, Sitansu S. PrincirJes of Relational Database Svstems. Englewood Cliffs, N. Y.: Prentice-Hall, Inc., Pratt, Philip J. Microcomputer Data Base Mana~ement Usimz dbase III Plus. Boston, MA Boyd & Fraser Publishing Co., Stamper, David and Wilson Price. Database Desire and Mana~ement: An A~plied Ap~roach. New York McGraw-Hill, Inc., CONCLUSION The study of forty real world databases showed that 4NF occurs more often than we previously believed. Data violating 5NF did not occur in any of the databases which may indicate that 5NF is only an academic issue, Because data violating 4NF was found to occur in over twenty percent of the organizations in the study, it is advisable that practitioners understand and apply the constraints for 4NF. It is also imperative that the rules for 4NF be emphasized in the teaching of normalization theory. ACKNOWLEDGEMENT The author wishes to thank Jeff Hoffer for su~esting this research project. REFERENCES 1. Courtney, James F. and David B. Paradice. Database Svstems for Management. St. Louis: Times Mh-ror/Mosby College Publishing Co., Date, C. J. An Introduction to Data Base m. 5th ed. Reading, MA: Addison-Wesley Publishing Co., Edwards, Joe B. High Performance Without Compromise} Datamation, ~, 13, (July 1, 1990), Elmasri, Ramez and Shamkant B. Navathe. Fundamentals of Database Svstems. Redwood City, CA: Benjamin/Cummings Publishing Co

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