Determinants are rich. Most of us are only familiar with linear algebraic methods, but as the amount of data becomes too big to fit in memory, we need novel methods such as yours. More promising is combinatorial random approaches (Las Vegas/Monte Carlo kind.)

So its basically a distributed equation solver, solves system of linear equation. At the core of system is solving determinant in trivial way but merging results back to calculate final value. Though we didnt do any rigorous benchmarks works decent.