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8.2. Specifications of the problem: identification of functions
8.2.1. Hierarchical menu
The frame of the study in which we place ourselves is the standard structure of
the hierarchical menu mentioned in section 8.3 (particularly in [BRE 98a]). Its tree-
like architecture consists of nodes and branches that establish parental relations
between the different nodes.
From a general point of view, the first node of the structure (generally
represented at the top) is called the “root” and is the starting point for the tree. Each
node inherits properties from the node placed directly above it (“parent” node) and
gives its properties to all the nodes that are placed directly below it in the hierarchy
(“child” nodes); furthermore, nodes that come from the same parent are called
“brothers” (or “sisters”) and an “ancestral” node is a node which is linked to all the
nodes situated on a lower level. In addition, a child only has a single direct parent,
which implies that there is a unique path from one point of the tree to another.
Figure 8.1 represents this hierarchical structure symbolically where: A is the root of
the tree; B is the parent of D and E; B and C are the children of A; F, G and H are
brothers (or sisters); and A is the ancestor of all the nodes of the tree, from B to L
(see [SHA 01], for more details on the formalisms of trees).
In the case that concerns us, the architecture and taxonomy of the tree are
slightly adapted and modified according to the application targeted. The nodes
represent families of content (called “menus”) and possess lower hierarchical levels
(“sub-menus”) the specific content of which therefore naturally inherits the content
of their ancestors. Similar to a classic library process that progress, for example, in
the following manner: Geography > World > Africa > Western Africa > Mali.
Moreover, the structure used for the application does not really have a root, since the
highest level already contains several menus. Finally, each level can be considered
as a list in its own right, therefore regrouping all the brother elements, in which it is
possible to move horizontally without having to go via the shared higher level: to go
back to the analogy of a library, it is thus possible to reach the different continents
without having to systematically go via the parent menu (World). However, the
structure respects one of the fundamental properties of the tree: the unique nature of
the path between two points of the tree. Indeed, each list is ordered and its progress
systematically begins from the first element; thus, still using the library analogy,
going to Oceania boils down to using the following path: Geography > World >
Africa / America / Asia / Europe / Oceania. Figure 8.2 specifies the hierarchical
structure adapted to the application targeted in the study.
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