# Fast Breadth-First Search in Still Less Space

## TL;DR

This paper presents a space-efficient algorithm for breadth-first search that operates in linear time using significantly less memory than traditional methods, making it suitable for large graphs.

## Contribution

It introduces a novel BFS algorithm that uses only about n log2 3 bits of memory, reducing space requirements while maintaining linear time complexity.

## Key findings

- BFS can be performed in O(n+m) time with minimal memory.
- The algorithm uses n log2 3 + O((log n)^2) bits of space.
- The approach improves space efficiency over existing BFS implementations.

## Abstract

It is shown that a breadth-first search in a directed or undirected graph with $n$ vertices and $m$ edges can be carried out in $O(n+m)$ time with $n\log_2 3+O((\log n)^2)$ bits of working memory.