Revisiting the Majority Problem: Average-Case Analysis with Arbitrarily Many Colours

TL;DR

This paper analyzes the average-case performance of three deterministic algorithms for the majority problem with many colours, providing heuristic insights and validating them through large-scale simulations.

Contribution

It offers the first heuristic average-case analysis for multiple colours in the majority problem and supports findings with extensive empirical simulations.

Findings

Heuristic analysis of three algorithms for many colours

Empirical validation through large-scale simulations

Insights into average-case performance beyond two colours

Abstract

The majority problem is a special case of the heavy hitters problem. Given a collection of coloured balls, the task is to identify the majority colour or state that no such colour exists. Whilst the special case of two-colours has been well studied, the average-case performance for arbitrarily many colours has not. In this paper, we present heuristic analysis of the average-case performance of three deterministic algorithms that appear in the literature. We empirically validate our analysis with large scale simulations.