In this work, we design algorithms for two fundamentally important and classical graph problems in the planted setting.

As scientists and engineers, we have long aimed at solving real-time problems such as detecting and localizing objects seen by our video recorder or at least something like Pokemon's Animedex.

Randomness is a remarkably powerful tool in the design of algorithms. By giving algorithms the ability to use random bits and letting them err with some small  probability, we can solve many computational problems with remarkable efficiency.

The problem of learning arithmetic circuits is the following: given a polynomial as a black box that is promised to have a small arithmetic circuit computing it, can we find this arithmetic circuit?