A Space and Time Efficient Coding Algorithm for LattÍce Computations

This paper presents an encoding algorithm to enable fast computation of the least upper bound (LUB) and greatest lower bound (GLB) of a partially ordered set. The algorithm presented reduces the LUB computation to an OR operation on the codes. The GLB computation is reduced essentially to an AND operation on the codes. The time complexity of our encoding algorithm is O(n + e) where n is the number of nodes and e is the number of edges. With respect to space requirements the algorithm presented gives good results for small lattices (code length was 50 bits for a 300 node lattice), but it gives truly remarkable results for larger lattices (e.g. for a 950 node lattice it used 110 bits)