Bogdán Zaválnij

Abstract This manuscript provides a comprehensive review of the Maximum Clique Problem, a computational problem that involves finding subsets of vertices in a graph that are all pairwise adjacent to each other. As such, this review is a continuation of the series of previous reviews from 1994, 1999 and 2014. The manuscript covers in a simple way classical algorithms and includes a review of recent developments in graph neural networks and quantum algorithms.

1. Introduction One way to classify statistical procedures is to divide them into exploratory and explanatory (or confirmatory) methods. The main purpose of the explanatory methods is to assess how strongly the data support a particular statistical hypothesis. The arguments are based on considerations from probability theory (frequentist or Bayesian). On the other hand, the exploratory methods typically have a more modest aim. They are concerned only with exploring the given data set.