We consider the problem of generating upper bounds for the probability of the union of events when the individual probabilities of the events as well as the probabilities of pairs of these events are known. By formulating the problem as a Linear Program, we can obtain bounds as objective function values corresponding to dual basic feasible solutions. The new upper bounds are based on underlying bipartite and threshold type graph structures.
Veneziani, Pierangela, "Graph-Based Upper Bounds for the Probability of the Union of Events" (2008). Mathematics Faculty Publications. 8.
Veneziani, P. (2008). Graph-Based Upper Bounds for the Probability of the Union of Events. Electronic Journal of Combinatorics, 15(1R), 1-11.
First published in Electronic Journal of Combinatorics in 2008, published by the American Mathematical Society