Defines an algorithm in which to traverse the components of a graph. A graph iterator operates by
repeatedly returing graph components to the caller. The order in which to return the components
is specific to the iterator. However,
most iterators follow the following conventions:
- Components are visited only once
- The next component to be returned is determined by the components that have been previously
visited
The following is an example of a GraphIterator. It returns nodes of a graph in a standard
Depth First Search order, starting from a specified node. The nodes have been numbered to
correspond to the iteration pattern.
* indicates source of traversal
In order to analyze the traversal, the following terms are defined:
The
Next Set of a traversal is the set of components that will be visited in a later stage
of the traversal.
The
Branch Set of an component
e is defined as the set of components that can be
visited in a later stage of the traversal as a direct result of visiting
e.
In most traversals, the two sets are related. The Next Set is built by analyzing the Branch Set
of the component being visited in the current stage of the traversal. Revisiting the above
example, a Depth First Search Traversal operates as follows:
- Each node is visited only once.
- The Next Set is organized as a Last In First Out Queue (Stack).
- At each stage, every node in the Branch Set that has not yet been visited is added to the
Next Set.
As well it is assumed that nodes related to a node are sorted in alphabetic order.
The following table summarizes the stages of the traversal:
| Stage |
Visited Node |
Branch Set |
Next Set |
Comment |
| 0 |
|
|
{A} |
Initial stage, iteration starts explicitly from A |
| 1 | A | {B,F} | {F,B} |
Related nodes added to Next Set in LIFO order. |
| 2 | F | {A,B} | {B,B} |
A already visited so not added to Next Set
B not yet visited so added to queue. |
| 3 | B | {A,C,D,E,F} | {B,E,D,C} |
A,F already visited so not added to Next Set |
| 4 | B | | {E,D,C} |
B already visited so ignore and move to next stage |
| 5 | E | {B} | {D,C} |
|
| 6 | D | {B,C} | {C,C} |
|
| 7 | C | {B,D} | {C} |
|
| 8 | C | | { } |
C already visited so ignore and move to next stage |
| 9 | | | { } |
Next set empty, iteration complete. |
At any stage of a travesal a branch may be
killed.When a branch is killed at a stage of an
iteration, no elements in the current
Branch Set are added to the
Next Set. This is
illustrated by revisiting the Depth First Search Iteration, but this time killing the branch at
node B. The following table summarizes the stages of the traversal:
| Stage |
Visited Node |
Branch Set |
Next Set |
Comment |
| 0 |
|
|
{A} |
Initial stage, iteration starts explicitly from A |
| 1 | A | {B,F} | {F,B} |
Related nodes added to Next Set in LIFO order. |
| 2 | F | {A,B} | {B,B} |
A already visited so not added to Next Set
B not yet visited so added to queue. |
| 3 | B | {A,C,D,E,F} | {B} |
Branch Killed. No nodes added to Next Set |
| 4 | B | | { } |
B already visited so ignore and move to next stage |
| 9 | | | { } |
Next set empty, iteration complete. |
In this example, killing the branch at node B results in nodes C, D, and E never being visited.