Reduction from Triangle Detection to Disjunctive Queries of Safety in Graphs

FROM: Triangle Detection TO: Disjunctive Queries of Safety in Graphs

Implications

assume: Strong Triangle
then: there is no combinatorial $O(n^{3-\epsilon})$ or $O((k \cdot n^{2})^{1-\epsilon})$ algorithm, for any $\epsilon > {0}$ for disjunctive safety (objectives or queries) in graphs.

Year

2016

Reference

Chatterjee, Krishnendu, et al. "Model and objective separation with conditional lower bounds: Disjunction is harder than conjunction." Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science. 2016.

https://dl.acm.org/doi/pdf/10.1145/2933575.2935304