Efficient algorithms on distributive lattices

We present several efficient algorithms on distributive lattices, They are based on a compact representation of the lattice, called the ideal tree. Th is allows us to exploit regularities in the structure of distributive latti ces. The algorithms include a linear-time algorithm to reconstruct the cove ring graph of a distributive lattice from its ideal tree, a linear-time inc remental algorithm far building the ideal lattice of a poset and a new incr emental algorithm for listing the ideals of a poset in a combinatorial Gray code manner in an H(1, 2) code. (C) 2001 Elsevier Science B,V. All rights reserved.