Using Hypercube Simulator:

The Hypercube Simulator tool calculates three things:

• The probability that the given hypercube is connected:  This means that each node in the hypercube is connected to every other node in the hypercube by at least one path. This is the least restrictive definition of a connected hypercube and uses a fully fault tolerant routing algorithm in order to test node to node connections.
• The probability that each lower order fully connected subcube is connected within the given hypercube:  A fully connected subcube of order N is defined as 2^N connected nodes each with N working links.  This is the most restrictive definition of a subcube, but it represents the most useful configuration.  Such a subcube would have most of the properties of an uninjured hypercube of dimension N.  This could run all algorithms designed for N dimension hypercubes.
• The probability that each lower order sparsely connected subcube is connected within the given hypercube:  A sparsely connected subcube of order N is defined as 2^N connected nodes each with as little as one working link.  This is the least restrictive definition of a subcube, but it illustrates the fault tolerant nature of a hypercube network.

The calculated values are output in the text area beneath the Run Simulation button.  The probabilities of each type of subcube are also represented in the two bar graphs located beneath the output text area.  Be sure to pay attention to the scale and boundary values of the bar graphs as they can change each time the simulation is run.

The link reliability is the average probability that a given link is working.  It can be changed to any decimal value between 0 and 1.0.  The hypercube dimension is the dimension of the hypercube to be simulated and can be changed to any value between 3 and 30.  However, it should be kept in mind that the simulation time will increase exponentially with the hypercube dimension, therefore, any simulation of a hypercube of dimension greater than 10 should be expected to take several minutes, with extremely large cubes taking hours.  The number of iterations is the number of randomly configured hypercubes which will be tested in order to calculate the probabilities.  Keep in mind that the more iterations used to more accurate the values will be, and the longer the simulation will take.  Be sure to choose a value accordingly.  Also, note that if the value does not change more than .1% in 500 iterations the simulation will stop, having reached a stable value, and the total number of completed iterations will be displayed in the output text area.   A progress bar is also located directly beneath the simulation button in order to track simulation performance and progress.