Beame et al. [ITCS 2018 & TALG 2021] introduced and used the Bipartite Independent Set (BIS) and Independent Set (IS) oracle access to an unknown, simple, unweighted and undirected graph and solved the edge estimation problem. The introduction of this oracle set forth a series of works in a short span of time that either solved open questions mentioned by Beame et al. or were generalizations of their work as in Dell and Lapinskas [STOC 2018], Dell, Lapinskas and Meeks [SODA 2020], Bhattacharya et al. [ISAAC 2019 & Theory Comput. Syst. 2021], and Chen et al. [SODA 2020]. Edge estimation using BIS can be done using polylogarithmic queries, while IS queries need sub-linear but more than polylogarithmic queries. Chen et al. improved Beame et al.'s upper bound result for edge estimation using IS and also showed an almost matching lower bound. Beame et al. in their introductory work asked a few open questions out of which one was on estimating structures of higher order than edges, like triangles and cliques, using BIS queries. Motivated by this question, we completely resolve the query complexity of estimating triangles using BIS oracle. While doing so, we prove a lower bound for an even stronger query oracle called Edge Emptiness (EE) oracle, recently introduced by Assadi, Chakrabarty and Khanna [ESA 2021] to test graph connectivity.

翻译：Beame et al. [ITCS 2018 & TALG 2021] 介绍并使用Bipartite独立赛事和独立赛事[SOD 2020]、 Bhattacharya et al. [ISAAC 2019 & Theory Comput. Syst. 2021] 和 Chen et al. [SOD 2020] 介绍并使用一个未知、简单、无重量和无方向的图表,并解决了边缘估计问题。 引入这一赛事后,在短短的时间内就提出了一系列工作,要么解决了Beame等人(ITS 2018 和Lapinskas [STOC 2018]、Dell、Lapinskas 和 Meeks [SODS 2020]、 Bhatthatcharyyalychary 等人(IS 2019 和The TheThe The Thereality complical etrial ) 的工程, 其入门上的结果几乎是更紧密的。