Such thing as a too much of a Tutor?

Last post I mentioned I would have some pictures for you this week, and I just know all my readers cant sleep without those graphs, I will fulfil my promise. But first, (wouldnt be as fun if I didnt make you wait), this week, its been mentioned that I spend too much time on my tutorials.

This might not sound bad but I now notice that several times a week I find myself writing additional material or small programs to help my students with the tutorials. I have also been developing a demo of a coursework for one course, which has taken more time than it should have.  Therefore, I hereby declare that I will refrain from this in future, and will keep to the expected 1hour 30mins extra time I am expected to give per tutorial. 

Now that time is an issue and I am drifting away from my studies, its time to get back into shape. I present to you, my latest results, comparing the different approximation techniques on the graph 3elt.

CA : Contraction Approximation
QT : Quad Tree Approximation (Barnes Hut / Yifan Hu)
ML : Standard Multilevel - No Approximation

3elt edge crossings at size 50	3elt runtime at size 50
3elt runtime at size 50 (excluding ML)
3elt edge crossings at size 250	3elt runtime at size 250

The results show that the contraction approximation is the fastest again (further testing show this is mostly due to not having to build the QuadTree structure). Unfortunately, the Quad Tree still provides better results for edge crossings. Below shows some results for the 3elt graph - excluding the ML algorithm (due to the time it would take to run the tests).

4elt edge crossings at size 50	4elt runtime at size 50
4elt edge crossings at size 200	4elt runtime at size 200

Similarly, these results show that the contraction approximation is faster and that the quad tree offers better quality. Note that in the size 50, the runtime appears to get smaller for quad tree, as the force multiplier is increased; if the results where to continue, it would most likely become faster than the contraction approximation (unfortunately for quad tree, the number of edge crossings increases hugely before this happens).

Using a measure of quality which applies to all graphs ( (E)(E-1)/ec ) I can see that quad tree continues to offer better results in smaller graphs, but when using 4elt, the difference becomes smaller and in some cases, the contraction approximation offers better quality.

3elt Quality	4elt Quality

If possible, I may run some additional tests on larger graphs (finan512 testing failed due to the problems exhibited with  QT before), which will identify whether edge contraction becomes more useful in larger graphs or whether this is just a coincidental case (in theory it would make sense due to the approximation using the graph structure but previously this assumption has been wrong).

Results from this will also help choose a useful default force multiplier for some graphs. Currently it appears the best parameters are using size 50 with a force multiplier between 1.0 and 50.0, however, from experience I know that with larger graphs, it is better to draw them using a larger output area with forces outside of this range.

Currently I am planning out/writing out my paper for this, based on these results. I do however feel more results are required, but for now, I can concentrate my writing on the theory.