The 3SUM problem asks if there are three integers $a,b,c$ summing to $0$ in a given set of $n$ integers of magnitude poly($n$). Patrascu (STOC '10) reduces solving 3SUM in time $n^{2-\Omega(1)}$ to listing $m$ triangles in a graph with $m$ edges in time $m^{4/3-\Omega(1)}$.
In this note we present ... more >>>

We show that if one can solve 3SUM on a set of size $n$
in time $n^{1+\epsilon}$ then one can list $t$ triangles in a
graph with $m$ edges in time $\tilde
O(m^{1+\epsilon}t^{1/3+\epsilon'})$ for any $\epsilon' > 0$. This is a
reversal of Patrascu's reduction from 3SUM to
listing triangles ... more >>>