We study the task of estimating the number of edges in a graph, where the access to the graph is provided via an independent set oracle. Independent set queries draw motivation from group testing and have applications to the complexity of decision versus counting problems. We give two algorithms to estimate the number of edges in an n -vertex graph, using (i) polylog( n ) bipartite independent set queries or (ii) n 2/3 polylog( n ) independent set queries.

中文翻译：

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独立集预言机的边缘估计

我们研究估计图中边数的任务，其中对图的访问是通过独立的集合 oracle 提供的。独立集合查询从组测试中汲取动力，并应用于决策与计数问题的复杂性。我们给出了两种算法来估计一个n-顶点图，使用 (i) polylog(n）二部独立集查询或（ii）n 2/3多对数（n) 独立集合查询。