Parameter hierarchy now with database and interactive visualization

I have recently worked on a major update to the parameter hierarchy, check it out here.

The parameter hierarchy tracks graph parameters, functions mapping a graph to a number, and their relations. That is, whether one parameter is bounded by a function of another parameter in every graph or whether one can find graphs where they are arbitrarily far apart from each other.

Tracking parameters and their relations has come up naturally in lots of research, particularly in parameterized algorithms research where you want to push tractability results to the smallest parameters that allow them. Currently the most active is probably hops. None of them seem to be as active as I would hope. Partly this is because of time constraints of the ones managing them, but partly I think this is because of the following: The data is either quite difficult to access, for example, in our previous parameter hierarchy where it was in a latex document, or isgci, where it is in a neat format, but the data themselves are not public, or in some format that’s difficult to understand or update such as in hops. This makes it difficult for people to contribute and puts the maintainers as points of failure.

With the recent update I tried to address these issues: For one, the format is a simple, human-readable json, available on the gitlab project. You can directly edit the database with an editor and be reasonably sure that it will work. In addition, I put convenient cli tools for updating the data. Second, I made a website that visualizes the hierarchy in a neat way, and tried to make it easy for contributors to suggest parameters and relations via this website: Once you click the corresponding features, you will be asked for the data, such as the reference where the parameter is from, the two parameters involved in a suggested relation, etc. Then you can send these data as a preformatted email to me and I can insert the data in a semi-automatic way. This hopefully lowers the bar for adding and correcting data, and the simple format should make it easy to fork.

I also always dreamt of a nice interactive visualization of the hierarchy and with this update it mostly became reality. It uses a custom framework for rendering the hierarchy diagram based on the Sugiyama framework with additional heuristics for minimizing crossings and a dynamic force-based layout. You can hide parameters you’re not interested in and even export a tikz (which is rudimentary at this point).

I imported all the data from isgci that I had and from hops, but this was quite a messy process. I’m still auditing the data to ensure everything is high quality, but I believe already in the current state it could be quite useful.

All of this would not have been possible without the latest update to Claude Code / Claude Opus 4.6. Codex helped, too, but it seemed much too narrow-minded to be really useful and wrote messy visualization code that it could not wrap its head around to fix.