We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under certain natural conditions on sets of preferences, a logarithmic number of queries with respect to accuracy is sufficient.
Grebennikov, Alexandr, et al. "Logarithmic algorithms for fair division problems." arXiv preprint arXiv:2112.13622 (2021).