Chapter 7

Summary of Templates

Table 7.1, Table 7.2, Table 7.3, Table 7.4 and Table 7.5 summarize the mathematical templates.

Table 7.1

Tree Templates

Template

Synopsis

UML diagram

Use when

Frequency

Hardcoded tree

Specifies a type sequence, one for each level of the hierarchy.

image

The levels in a tree are known and ordered.

Seldom

Simple tree

Treats all nodes the same.

image

A tree concerns only data structure.

Common

Structured tree

Differentiates leaf nodes from branch nodes.

image

Branch nodes and leaf nodes differ.

Common

Overlapping tree

Permits a node to belong to multiple trees.

image

A node can belong to more than one tree.

Occasional

Tree changing over time

Stores variants of a tree over time.

image

There is history to record.

Occasional

Degenerate node and edge

Groups a parent with its children.

image

There is data for the parent-child grouping.

Rare

Table 7.2

Directed Graph Templates

Template

Synopsis

UML diagram

Use when

Frequency

Simple DG

Treats all nodes the same.

image

Edges are unimportant; nodes have the same kind of data. The DG is acyclic.

Occasional

Structured DG

Differentiates leaf nodes from branch nodes.

image

Edges are unimportant; branch nodes and leaf nodes have different data. The DG is acyclic.

Occasional

Node-edge DG

Treats nodes and edges as peers.

image

Nodes and edges can both have data; there can be multiple edges between a pair of nodes.

Common

Connection DG

Promotes a node-edge connection to an entity type.

image

Connections have data.

Occasional

Simple DG changing over time

Stores variants of a DG over time.

image

There is history to record; edges are unimportant. The DG is acyclic.

Seldom

Node-edge DG changing over time

Stores variants of a DG over time.

image

There is history to record; edges are important.

Occasional

Table 7.3

Undirected Graph Templates

Template

Synopsis

UML diagram

Use when

Frequency

Node-edge UDG

Treats nodes and edges as peers.

image

No edge connects to the same node.

Occasional

Connection UDG

Promotes a node-edge connection to an entity type.

image

Connections have data or an edge connects to the same node.

Occasional

UDG changing over time

Stores variants of a UDG over time.

image

There is history to record.

Seldom

Table 7.4

Item Description Templates

Template

Synopsis

UML diagram

Use when

Frequency

Item description

Relates data and metadata in the same model.

image

The same model relates data and metadata.

Frequent

Homomorphism

Expresses an analogy between two item description templates.

image

Item description templates are involved in an analogy.

Occasional

Table 7.5

Star Schema Template

Template

Synopsis

UML diagram

Use when

Frequency

Star schema

Represents data as facts that are bound to dimensions.

image

There must be a flexible structure for querying data.

Occasional (frequent for data warehouse)

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