A simpler sublinear algorithm for approximating the triangle count

A recent result of Eden, Levi, and Ron (ECCC 2015) provides a sublinear time algorithm to estimate the number of triangles in a graph. Given an undirected graph G, one can query the degree of a vertex, the existence of an edge between vertices, and the ith neighbor of a vertex. Suppose the graph has n vertices, m edges, and t triangles. In this model, Eden et al provided a O(poly(ε logn)(n/t+m/t)) time algorithm to get a (1+ε)-multiplicative approximation for t, the triangle count. This paper provides a simpler algorithm with the same running time (up to differences in the poly(ε logn) factor) that has a substantially simpler analysis.