On Triangle Estimation using Tripartite Independent Set Queries
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 \emph{the number of triangles on any edge in the graph is polylogarithmically bounded}. Our query oracle {\em Tripartite Independent Set} (TIS) takes three disjoint sets of vertices , and 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 \emph{group queries} (Ron and Tsur, ACM ToCT, 2016; Dell and Lapinskas, STOC 2018) and in particular is inspired by the {\em Bipartite Independent Set} (BIS) query oracle of Beame {\em et al.} (ITCS 2018). We extend the algorithmic framework of Beame {\em et al.}, with \tis replacing \bis, for approximately counting triangles in graphs.
Cite
@article{arxiv.1808.00691,
title = {On Triangle Estimation using Tripartite Independent Set Queries},
author = {Anup Bhattacharya and Arijit Bishnu and Arijit Ghosh and Gopinath Mishra},
journal= {arXiv preprint arXiv:1808.00691},
year = {2020}
}
Comments
27 pages. A preliminary version has been appeared in ISAAC'2019. This version contains improved bound on query complexity