Spectral recovery of a planted triangle-dense subgraph (opens in new tab)

Given a simple graph on $n$ vertices and a parameter $k$, the triangle-densest-$k$-subgraph problem is known to be computationally hard in the worst case. To circumvent the computational hardness, we study an average-case model where a triangle-dense subgraph on $k$ vertices is planted in an Erd\H{o}s-R\'enyi random graph on $n$ vertices. For the recovery of the planted subgraph, we propose a simple spectral algorithm and a semidefinite program,...