Amit Levi

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

Estimating the density of intermediate size KBOs from considerations of volatile retention

0<\epsilon<1

H-atmospheres of Icy Super-Earths Formed In Situ in the Outer Solar System: An Application to a Possible Planet Nine

, the algorithm provides an estimate

Corona-like atmospheric escape from KBOs. I. Gas dynamics

\widehat{t}

Corona-like atmospheric escape from KBOs: II. The behavior of aerosols

such that, with high constant probability,

Approximately Counting Triangles in Sublinear Time.

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

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

, where

Sublinear-Time Quadratic Minimization via Spectral Decomposition of Matrices.

t

Lower Bounds for Tolerant Junta and Unateness Testing via Rejection Sampling of Graphs.

is the number of triangles in the graph

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

G