## Successive Shortest Path-Program

### What is SSP

Successive Shortest Path (or SSP) is a mathematical algorithm that optimizes a network with cost and capacity constraints.
To use this you will need a graph (in the graph theoretic sense) with nodes and edges.

Each edge needs both a capacity and a cost. Think of it like roads.
Each road has a certain length - this would be the cost, because you would want people to drive as little as possible.

However each road also can only contain a certain amount of cars - this would be the capacity.

The SSP seeks to find the least costly route for TOTAL amount of cars, which can be quite bothersome in some complex road networks.

### Why did you make this?

I created this at my second semester at Aalborg University.I had an 'elective course' (though they only recommended this course - a forced free choice) in Object-Oriented Programming - specifically C#. And I thought "I am never going to use C# in my math-education if I don't use it now!" - so I made this program for our project.

Our project aimed to create the most SIMILAR groups of psychiatric patients - so we would have groups in which the patients would be the most comparable.

We didn't have patient data though, but we had been speaking with "The Psychiatry" about their needs.

It was a fun exercise, because SSP is not directly suited for this, so you would have to generate the graph/network to your needs.

### How do I use this program?

First you need a Windows computer - or a software that can run executable-files. Then you of course need a graph you want to run from one vertex to another. You got that? Then you just have to edit the "Liste.txt" for your needs (it is written in this file, how to do it).Then you should just run the executable and a commandoprompt will then give you the result. The entire result is also printed into the SSP-information.txt!

There you go. I actually had created a graphical version of this at some point, but it is lost.