Celebrity

In computer science, the term „celebrity“ often refers to a specific type of problem in the context of social networks and graph theory. The celebrity problem involves identifying an individual within a group who is known by everyone but does not know anyone else in that group.

Formally, a celebrity is defined as a person ‚C‘ in a group of ‚N‘ people such that:
1. Every other person in the group knows ‚C‘.
2. ‚C‘ does not know any other person in the group.

This concept can be represented using a directed graph, where nodes represent individuals and edges represent knowledge, i.e., if person A knows person B, there is a directed edge from A to B. The goal is to efficiently determine if there is a celebrity in the group, and if so, identify them. The problem can be solved using various algorithms, usually involving a combination of pairwise comparisons to reduce the number of candidates rapidly, typically in O(N) time complexity.

The celebrity problem serves as an example in algorithm design and can be applied to various scenarios in social network analysis, network theory, and related fields.