# Enumerating Range Modes

## TL;DR

This paper introduces efficient algorithms for the range mode problem and its enumeration variant, optimizing query times especially for small maximum frequencies, filling a gap in existing solutions.

## Contribution

It presents the first efficient algorithms for the range mode enumeration problem, with query times linear to output size and applicable to small maximum frequency cases.

## Key findings

- Algorithms achieve linear query time relative to output size.
- Efficient solutions for small maximum frequency scenarios.
- Addresses a previously unsolved problem in range mode enumeration.

## Abstract

We consider the range mode problem where given a sequence and a query range in it, we want to find items with maximum frequency in the range. We give time- and space- efficient algorithms for this problem. Our algorithms are efficient for small maximum frequency cases. We also consider a natural generalization of the problem: the range mode enumeration problem, for which there has been no known efficient algorithms. Our algorithms have query time complexities which is linear to the output size plus small terms.