Improve line plot visualisation I want to improve the graphic



that I created with R's ggplot2. The graphic is for a scientific publication. These are the runtime of 12 algorithms. There are four at the top, four in the middle and four at the bottom. They are not necessarily related to each other. It is very hard to discern the different colours from each other.

The main point that I want to drive home is that there are four that are slow, four that are middle fast, and four that are fast. Indeed, the groups should be more or less equally fast, and the fact that they differ is mostly due to the fact, that we talk about runtime (which always differs).

How can I improve the plot such that I drive home the main point without being distracted by the many colour, but possibly still have differentiation within the three groups?

Maybe it is not smart to keep the differentiation in the first place?

I would like to keep the line plot, but I am open to alternative suggestions if there are really good ideas out there.
You already made it log scale which would have been my first idea. How about use lattice to make it three plots with different Y start and end? Each plot should have a center point that covers one of the three groupings you have and you can stack them 1x3 (vertically).