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Published byVeronica Dennett Modified about 1 year ago

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Multivalued Dependency (MVD) & Join Dependency (JD) The third type of DD is related to the decomposition restriction on a single schema. This includes multivalued dependency (MVD) and join dependency (JD)

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Multivalued Dependency (MVD) Notation: MVD ├ A B Example –In the relation pattern. An MVD dept course is satisfied. t1 [dept] = t2 [dept] = t3 [dept] = t4 [dept] = 1 t3 [course] = t1 [course] = COMP104 t4 [course] = t2[course] = COMP171 Also, t5 [dept] = t6 [dept] = t7 [dept] = t8 [dept] = 2 t7 [course] = t5 [course] = ELEC102 t8 [course] = t6 [course] = ELEC151

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Multivalued Dependency (MVD) sidsnamesprogramsdept 1001stud_ABEng(COMP)1 1002stud_BBEng(COMP)1 1003stud_CBEng(ELEC)2 1004stud_DBEng(ELEC)2 deptcourse 1COMP104 1COMP171 2ELEC102 2ELEC151 student requirement

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Multivalued Dependency (MVD) studentdeptcourse 10011COMP COMP COMP COMP ELEC ELEC ELEC ELEC151 Two students in the same department take the same courses pattern

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Multivalued Dependency (MVD) Example (cont’d) –In other words, students in the same department follow the same study pattern to take courses. –Students (1001, 1002) in the Computer Sci. department take COMP104 and COMP171 –and those (1003, 1004) in the Electronic Eng. department take ELEC102 and ELEC151. Example

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Join Dependency (JD) JD is the general version of MVD If the schema can be broken up into n (n≥1) or more schema losslessly, the schema obeys JD. particularly, when n=1, it is the trivial case. when n=2, it is actually MVD.

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Join Dependency (JD) Example –In the relation enrollment –JD ((student, course), (course, lecturer), (student, lecturer)) holds, –but JD ((student,course), (course,lecturer)) does not. studentcourselecturer 1001COMP COMP COMP COMP ELEC ELEC ELEC ELEC1516 enrollment

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Join Dependency (JD) –Decompose the relation enrollment into 3 relations as follows CourseLecturer COMP COMP1713 ELEC1024 ELEC StudentLecturer StudentCourse 1001COMP COMP COMP COMP ELEC ELEC ELEC ELEC151

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Join Dependency (JD) –When the three relations are joined back together, it will be the same as before decomposing. –But joining the first two relations ((student, course), (course, lecturer)) would generate some spurious results. –The natural join is as shown in the next slide

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Join Dependency (JD) StudentCourseLecturer 1001COMP COMP COMP COMP COMP COMP ELEC ELEC ELEC ELEC ELEC ELEC1516 The tuples with red values are spurious. They do not exist in the original enrollment relation. Therefore the JD of joining these two relations does not hold.

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