We study a query model of computation in which an n-vertex k-hypergraph can be accessed only via its independence oracle or via its colourful independence oracle, and each oracle query may incur a cost depending on the size of the query. In each of these models, we obtain oracle algorithms to approximately count the hypergraph's edges, and we unconditionally prove that no oracle algorithm for this problem can have significantly smaller worst-case oracle cost than our algorithms.

翻译：我们研究一种计算查询模型，其中n顶点k超图只能通过其独立预言机或彩色独立预言机访问，且每次预言机查询可能产生与查询大小相关的成本。在每种模型中，我们获得了近似计算超图边数量的预言机算法，并无条件证明：对于该问题，任何预言机算法在最坏情况下的预言机成本都无法显著小于我们的算法。