On Triangle Estimation Using Tripartite Independent Set Queries

Article Type

Research Article

Publication Title

Theory of Computing Systems

Abstract

Estimating the number of triangles in a graph is one of the most fundamental problems in sublinear algorithms. In this work, we provide an algorithm that approximately counts the number of triangles in a graph using only polylogarithmic queries when the number of triangles on any edge in the graph is polylogarithmically bounded. Our query oracle Tripartite Independent Set (TIS) takes three disjoint sets of vertices A, B and C as inputs, and answers whether there exists a triangle having one endpoint in each of these three sets. Our query model generally belongs to the class of group queries (Ron and Tsur ACM Trans. Comput. Theory 8(4), 15, 2016; Dell and Lapinskas 2018) and in particular is inspired by the Bipartite Independent Set (BIS) query oracle of Beame et al. (2018). We extend the algorithmic framework of Beame et al., with TIS replacing BIS, for approximately counting triangles in graphs.

First Page

1165

Last Page

1192

DOI

10.1007/s00224-021-10043-y

Publication Date

11-1-2021

Comments

Open Access, Green

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