Dynamic maintenance of the transitive closure in disjunctive graphs

Abstract

We propose an approach with feasible space requirement to maintain the transitive closure of a class of hypergraphs called OR-graphs. OR-graphs are equivalent to disjunctive deductive databases where disjunctions are limited to one attribute in each OR-table. It has been shown that query processing in disjunctive deductive databases grows into CoNP with very simple examples, but few attempts have been made, as is done in this paper, to obtain classes of disjunctive databases and queries for which efficient algorithms exist. Polynomial time algorithms are presented to compute the transitive closure of OR-graphs and to handle dynamic insertions and deletions. With algorithms for insertions and deletions, we provide a simple but efficient technique to solve the failure set problem in reliability models, which is equivalent to finding the closure of an arbitrary non-empty set of simple nodes. We also show that a minimal extension to OR-graphs makes the computational complexity of the transitive closure CoNP-complete.