Algebraic Structure Discovery for Real World Combinatorial Optimisation Problems: A General Framework from Abstract Algebra to Quotient Space Learning

ArXi:2604.04941v1 Announce Type: new Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identifies algebraic structure, (ii) formalises operations, (iii) constructs quotient spaces that collapse redundant representations, and (i) optimises directly over these reduced spaces. Across a broad family of rule-combination tasks (e.g., patient subgroup discovery and rule-based molecular screening), conjunctive rules form a monoid.