Talya Eden

Approximately Counting Triangles in Sublinear Time

We consider the problem of estimating the number of triangles in a graph. This problem has been extensively studied in both theory and practice, but all existing algorithms read the entire graph. In this work we design a sublinear-time algorithm for approximating the number of triangles in a graph, where the algorithm is given query access to the graph. The allowed queries are degree queries, vertex-pair queries, and neighbor queries. We show that for any given approximation parameter

On Sampling Edges Almost Uniformly

0<\epsilon<1

On approximating the number of k-cliques in sublinear time

, the algorithm provides an estimate

Provable and practical approximations for the degree distribution using sublinear graph samples

\widehat{t}

Sublinear Time Estimation of Degree Distribution Moments: The Degeneracy Connection.

such that, with high constant probability,

Sublinear Time Estimation of Degree Distribution Moments: The Arboricity Connection.

(1-\epsilon)\cdot t< \widehat{t}<(1+\epsilon)\cdot t

Approximately Counting Triangles in Sublinear Time.

, where

Testing bounded arboricity

t

Tolerant junta testing and the connection to submodular optimization and function isomorphism

is the number of triangles in the graph

Tolerant Junta Testing and the Connection to Submodular Optimization and Function Isomorphism.

G