I\'m writing a reasonably complex web application. The Python backend runs an algorithm whose state depends on data stored in several interrelated database tables which does not
Be cautious of premature optimization.
Addition: The "Python backend runs an algorithm whose state..." is the session in the web framework. That's it. Let the Django framework maintain session state in cache. Period.
"The algorithm's per-user state undergoes many small changes as a user works with the application." Most web frameworks offer a cached session object. Often it is very high performance. See Django's session documentation for this.
Advice. [Revised]
It appears you have something that works. Leverage to learn your framework, learn the tools, and learn what knobs you can turn without breaking a sweat. Specifically, using session state.
Second, fiddle with caching, session management, and things that are easy to adjust, and see if you have enough speed. Find out whether MySQL socket or named pipe is faster by trying them out. These are the no-programming optimizations.
Third, measure performance to find your actual bottleneck. Be prepared to provide (and defend) the measurements as fine-grained enough to be useful and stable enough to providing meaningful comparison of alternatives.
For example, show the performance difference between persistent sessions and cached sessions.