A lattice-based representation of independence relations for efficient closure computation

Independence relations in general include exponentially many statements of independence, that is, exponential in the number of variables involved. These relations are typically characterised however, by a small set of such statements and an associated set of derivation rules. While various computational problems on independence relations can be solved by manipulating these smaller sets without the need to explicitly generate the full relation, existing algorithms for constructing these sets are associated with often prohibitively high running times. In this paper, we introduce a lattice structure for organising sets of independence statements and show that current algorithms are rendered computationally less demanding by exploiting new insights in the structural properties of independence gained from this lattice organisation. By means of a range of experimental results, we subsequently demonstrate that through the lattice organisation indeed a substantial gain in efficiency is achieved for fast-closure computation of semi-graphoid independence relations in practice.