Improved Inclusion-Exclusion Identities and Bonferroni Inequalities with Reliability Applications

Source abstract

This paper establishes a connection between the theory of convex geometries, the principle of inclusion-exclusion, and the topological concept of an abstract tube. In particular, it is shown that convex geometries give rise to improved inclusion-exclusion identities and improved Bonferroni inequalities. In this way, several known results from the literature are rediscovered in a concise and unified way. The results are applied in identifying a new class of hypergraphs for which the reliability covering problem can be solved in polynomial time.