Symmetry reduction is a well studied subject in geometric mechanics, where symmetries are usually described as an invariance under an action of a Lie group.

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.