Lower bounds for graph reconstruction with maximal independent set queries

We investigate the number of maximal independent set queries required to reconstruct the edges of a hidden graph. We show that randomised adaptive algorithms need at least Ω(Δ² log(n / Δ) / log Δ) queries to reconstruct n-vertex graphs of maximum degree Δ with success probability at least $1/2$, and we further improve this lower bound to Ω(Δ² log(n / Δ)) for randomised non-adaptive algorithms. We also prove that deterministic non-adaptive algorithms require at least Ω(Δ³ log n / log Δ) queries. This improves bounds of Konrad, O'Sullivan, and Traistaru, and answers one of their questions. The proof of the lower bound for deterministic non-adaptive algorithms relies on a connection to cover-free families, for which we also improve known bounds.