Lower bounds for graph reconstruction with maximal independent set queries
| Autor: | Michel, Lukas, Scott, Alex |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\Omega(\Delta^2 \log(n / \Delta) / \log \Delta)$ queries to reconstruct $n$-vertex graphs of maximum degree $\Delta$ with success probability at least $1/2$, and we further improve this lower bound to $\Omega(\Delta^2 \log(n / \Delta))$ for randomised non-adaptive algorithms. We also prove that deterministic non-adaptive algorithms require at least $\Omega(\Delta^3 \log n / \log \Delta)$ 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. Comment: 12 pages |
| Databáze: | arXiv |
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