A space-and-time-efficient coding algorithm for lattice computations

We present an encoding algorithm for lattices that significantly reduces space requirements while allowing fast computations of least upper bounds and greatest lower bounds of pairs of elements. We analyze the algorithms for encoding, LUB and GLB computations, and prove their correctness. Empirical experiments reveal that our method is significantly more space efficient than the transitive closure method, and the saving becomes increasingly more important as the size of the lattice increases. Index Terms - Lattices, least upper bound, greatest lower bound, encoding algorithm, partially ordered sets