Efficient Computation of Minimal Point Algebra Constraints by Metagraph Closure

Computing the minimal network (or minimal CSP) representation of a given set of constraints over the Point Algebra (PA) is a fundamental reasoning problem. In this paper we propose a new approach to solving this task which exploits the timegraph representation of a CSP over PA. A timegraph is a graph partitioned into a set of chains on which the search is supported by a metagraph data structure. We introduce a new algorithm that, by making a particular closure of the metagraph, extends the timegraph with information that supports the derivation of the strongest implied constraint between any pair of point variables in constant time. The extended timegraph can be used as a representation of the minimal CSP. We also compare our method and known techniques for computing minimal CSPs over PA. For CSPs that are sparse or exhibit chain structure, our approach has a better worstcase time complexity. Moreover, an experimental analysis indicates that the performance improvements of our approach are practically very significant. This is the case especially for CSPs with a chain structure, but also for randomly generated (both sparse and dense) CSPs.