The original database may be rebuilt from the subfragmentations and the aliases. The fragmentation of the given relational database by group of the repeated values of the attributes will save the needed memory, increase the processing speed of data. This work has been applied in people’s committee of Hatay province and its districts and precints. | ’ Tap ch´ Tin hoc v` Diˆu khiˆn hoc, , (2008), 3–11 ı e e . . a ` . ON THE DENSE FAMILIES OF DATABASE RELATIONS VU DUC THI1 , NGUYEN HOANG SON2 1 Institute of Information Technology, VAST of Mathematics, College of Sciences, Hue University 2 Department Abstract. The relational data model was defined by Codd [3] in 1970. Functional dependencies and minimal keys are very important concepts in the relational data model. The dense families of database relations were introduced by J¨rvinen [5] (2001), who has characterized functional dependencies and a minimal keys of relations in terms of dense families. The aim of this paper is to continue investigating some properties of dense families of database relations and their applications. We give necessary and sufficient conditions for an arbitrary family to be R− dense. We prove that for a given relation R the equality set ER is an R−dense family. We also propose an effective algorithm finding all minimal keys of a given relation R. Finally, some related problems are also studied in this paper. ´ ´ ’ T´m t˘t. Mˆ h` d˜. liˆu quan hˆ dˆ xuˆt Codd [3] v`o n˘m 1970. Phu thuˆc h`m v` o a o ınh u e e e a a a o a a . . . ` . . ´ ’ ´ kho´ tˆi tiˆu l` nh˜.ng kh´i niˆm rˆt quan trong trong mˆ h` d˜. liˆu quan hˆ. Ho tr` mˆt cua a o e a u a e a o ınh u e e u a ’ . . . . . . ’ u e ’ a o e a a o quan hˆ trong co. so. d˜. liˆu gi´.i thiˆu J¨rvinen [5] (2001). J¨rvinen d˘c phu thuˆc e . . . . . . . ’ ´ ’ ´ ’ h`m v` kho´ tˆi tiˆu cua quan hˆ theo quan diˆm ho tr` mˆt. Muc tiˆu b`i b´o l` tiˆp tuc nghiˆn a a a o e e e e a a a e . e . . u a . . ´ ’ c´.u mˆt sˆ t´ chˆt cua ho tr` mˆt cua quan hˆ, v` dung cua n´. Ch´ ng tˆi ra mˆt sˆ u o o ınh a ’ e a´ o u o o o . ´ . u a ’ . . . . ´ ’ o . a y a . ` ` u kiˆn cˆn v` du dˆ mˆt ho bˆt k` l` ho R− tr` mˆt. Ch´ ng tˆi ch´.ng minh r˘ ng v´.i mˆt quan ` ´ diˆ e e a a ’ e . u a u o u a o o . . . hˆ cho R tˆp b˘ ng nhau ER l` mˆt ho R− tr` mˆt. Ch´ ng
