Find the Shortest Path between two nodes in a Graph
Contents
Find the Shortest Path between two nodes in a Graph................................................................................ 1
The Problem .............................................................................................................................................. 1
The Solution .............................................................................................................................................. 2
The Rule Flow ............................................................................................................................................ 3
Connect Two Edges to form a simple path ........................................................................................... 3
Extend Paths ......................................................................................................................................... 4
Remove Unwanted Paths...................................................................................................................... 4
Remove all but the shortest path(s) ..................................................................................................... 5
Test Case ................................................................................................................................................... 6
Drawing a diagram of the Graph using Corticon ...................................................................................... 7
Assemble Graph Expression .................................................................................................................. 7
Draw Graph Automatically.................................................................................................................... 8
Automating the Entire process ................................................................................................................. 8
WriteFile................................................................................................................................................ 9
RunCommand ....................................................................................................................................... 9
The Problem
Given a graph such as this
Find the shortest path connecting any two specified nodes.
For example the shortest path between a and e is a-b-e (3)
The Solution
First we need a suitable vocabulary for defining the graph.
For example we could simply define a set of edges:
that specifies the distance between two nodes.
And a set of paths that connect multiple nodes:
where the attribute ‘via’ contains a list of the nodes visited.
For example
So how do we generate the Path objects from the Edge objects and find the one that has the shortest
distance?
The Rule Flow
Connect Two Edges to form a simple path
Implementation
Extend Paths
Remove Unwanted Paths
We need this additional entity in the vocabulary now:
If type is not ‘shortest’ then all paths from start to end will be listed.
Also, by omitting the Request object entirely we can get all possible paths between every pair of nodes.
Remove all but the shortest path(s)
Notice that in the implementation we have moved the test for ‘shortest’ to the filter and made it a
precondition. That means this rule sheet does not even execute when type is other than ‘shortest’.
This doesn’t change the functionality but could improve efficiency if you are not looking for the shortest
in a large graph. If there is no Request object this rule sheet will not execute.
Test Case
But how did we get Corticon to draw a picture of the graph?
Drawing a diagram of the Graph using Corticon
Assemble Graph Expression
In my Corticon Studio I have a couple of extended operators that can export this code and run the
Graphviz program to generate the picture. If you try running the rule above you probably won’t have my
extended operators.
However you can still draw the pictures as follows:
1.
2.
3.
4.
Download and install Graphviz (it’s free)
Start Graphviz
Copy/paste the string for the chart into Graphviz
Run graphviz
Draw Graph Automatically
Notes.
1.
2.
3.
4.
you will need an instance of Graph in your payload
The destination folder must already be created
You will need to download and install Graphviz
You will also need two extended operators
Automating the Entire process
If you want to add functionality to Studio to generate the picture for you here’s what you will need to
do:
1. Read the documentation on creating extended operators
2. Create two operators
a. WRITEFILE – to write the chart string to a text file
b. RUNCOMMAND – to run any command
The entity called ExtendedOperator simply provides a result attribute that can be assigned when the
extended operator is executed.
You will also need to write these operators in Java.
Here’s how I implemented them
WriteFile
I use the return value to indicate success or failure.
RunCommand
As you can see the java code is not complex but you will have to package these operators so they can be
accessed by Studio.
That topic is a bit outside this article but is covered in the Corticon documentation.
When you are done your extended operators will show up something like this: