High quality reverb algorithm
You need to generate early reflections with a few taps of delays (= convolution with the sum of a handful of diracs) ; and the "tail" with what is usually implemented with a network of all-pass (AP) and comb filters.

The first part is trivial to implement but difficult to get to sound right. It might help to look at the positioning of peaks at the head of pre-recorded impulse responses to get an idea of what kind of responses are "natural". It's hard to make it easily parametrizable by a few settings, though you could get away with it by offering a bunch of presets for this part to get an "hybrid" reverb à la Virsyn Reflect.

The tail is where algorithmic reverbs shine (no pun intended), since it is easy to parametrize. The grandfather of algorithmic reverbs is Schroeder's algorithm. Note that it only generates a "tail", not early reflections - you could augment it with a few taps of delays to give it a head. It does not sound very good (very "grainy") but it's a decent start - with that you have something to mess with and it helps understanding the impact of each parameter. Many praised algorithmic reverbs, especially those from the 80s (Lexicon, Eventide, Publison) are just finely tuned topologies of all-pass filters and comb filters. I suspect this involved a lot of trial and error by trained ears who got very good at figuring out how changes in parameters or topology would sound, rather than any scientific approach. Here is another interesting read - showing Keith Barr's favorite reverb topology. The original midiverb might not be your definition of "high quality algorithmic reverb", but it sounded sweet, and it puts thing in perspective to know it was made with a "dsp" only capable of MACs with coefficients of 0.5...

Valhalla room is my favorite software algorithmic reverb - take some time to read its developer's blog to find inspiration about the kind of things that help getting it right.