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I know that associations in class diagram can be bi-directional or directional. We refer to this as navigability. I am not sure to fully understand what it means.

Please consider the following example :

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Does the navigability in the example meant that we read this association as "one order detail is related to one item " and that we cannot read it in the opposite direction as for one Item it can have zero to many Order item ? Finally , how is navigability implemented as a code ?

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Navigability means according to the UML specifications:

that instances participating in links at runtime (instances of an Association) can be accessed efficiently from instances at the other ends of the Association. The precise mechanism by which such efficient access is achieved is implementation specific. If an end is not navigable, access from the other ends may or may not be possible, and if it is, it might not be efficient.

In your example, this means that:

  • the association can be read in both ways; navigability does not change the fact that there is an association with two sides;

  • an instance of OrderDetail can easily and efficiently find the associated Item object;

  • it is not guaranteed that Item could find all its associated OrderDetails, and if it could, it might not be efficient;

  • navigability has nothing to do with the multiplicity.

There is no rule about how to implement such a link. This is completely implementation dependent. Examples for your case:

  • In a RDBMS, an OrderDetailTable would have a mandatory ItemId column with the Id of the related Item, and the ItemTable would have Id as primary key. As a consequence, it would be extremely efficient to find the Item fir navigation. It would also be possbile to find all the OrderDetails that are related to an Item, but it might not be as efficient if the necessary indexes are not created.
  • In Java, the OrderDetail class could have a integer member ItemId. You could have an ItemRepository class with a method findById() that would return for a given integer the corresponding Item instance
  • In C++ you could have in the OrderDetail class a member that points to a specific Item. In this case, the opposite navigation is practically impossible if there isn't a pointer in the other direction.

As you see, this in very dependent of the implementation language, the related idioms and techniques chosen (e.g. integer id vs pointer). It also depends on the multiplicities, the kind of ownership, as well as access path designed for other associated classes.

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