MVD or multivalued dependency means that for a single value of attribute ‘a’ multiple values of attribute ‘b’ exist. We write it as,
a --> --> b
It is read as: a is multi-valued dependent on b.
Suppose a person named Geeks is working on 2 projects Microsoft and Oracle and has 2 hobbies namely Reading and Music. This can be expressed in a tabular format in the following way.
Project and Hobby are multivalued attributes as they have more than one value for a single person i.e., Geeks.
Multi Valued Dependency (MVD) :
We can say that multivalued dependency exists if the following conditions are met.
Conditions for MVD :
Any attribute say a multiple define another attribute b; if any legal relation r(R), for all pairs of tuples t1 and t2 in r, such that,
t1[a] = t2[a]
Then there exists t3 and t4 in r such that.
t1[a] = t2[a] = t3[a] = t4[a] t1[b] = t3[b]; t2[b] = t4[b] t1 = t4; t2 = t3
Then multivalued (MVD) dependency exists.
To check the MVD in given table, we apply the conditions stated above and we check it with the values in the given table.
Condition-1 for MVD –
t1[a] = t2[a] = t3[a] = t4[a]
Finding from table,
t1[a] = t2[a] = t3[a] = t4[a] = Geeks
So, condition 1 is Satisfied.
Condition-2 for MVD –
t1[b] = t3[b] And t2[b] = t4[b]
Finding from table,
t1[b] = t3[b] = MS And t2[b] = t4[b] = Oracle
So, condition 2 is Satisfied.
Condition-3 for MVD –
t1 = t4 And t2=t3
Finding from table,
t1 = t4 = Reading And t2 = t3 = Music
So, condition 3 is Satisfied.
All conditions are satisfied, therefore,
a --> --> b
According to table we have got,
name --> --> project
And for,
a --> --> C
We get,
name --> --> hobby
Hence, we know that MVD exists in the above table and it can be stated by,
name --> --> project name --> --> hobby
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