On non-adaptive majority problems of large query size

TL;DR

This paper investigates the non-adaptive majority problem where all queries are asked simultaneously to identify a ball from the larger color class or determine equal sizes, extending understanding beyond the adaptive query setting.

Contribution

It introduces the non-adaptive version of the majority problem with large query sizes and analyzes its complexity and query requirements.

Findings

Derived bounds for the number of queries needed

Compared non-adaptive and adaptive query complexities

Provided algorithms for non-adaptive majority detection

Abstract

We are given $n$ balls and an unknown coloring of them with two colors. Our goal is to find a ball that belongs to the larger color class, or show that the color classes have the same size. We can ask sets of $k$ balls as queries, and the problem has different variants, according to what the answers to the queries can be. These questions has attracted several researchers, but the focus of most research was the adaptive version, where queries are decided sequentially, after learning the answer to the previous query. Here we study the non-adaptive version, where all the queries have to be asked at the same time.