# A New Fast Unweighted All-pairs Shortest Path Search Algorithm Based on Pruning by Shortest Path Trees

## TL;DR

This paper introduces a novel unweighted all-pairs shortest path algorithm that leverages shortest path trees to significantly reduce vertex access, outperforming traditional BFS in speed.

## Contribution

The proposed algorithm uses shortest path trees to prune searches, drastically lowering average vertex accesses compared to BFS in unweighted graphs.

## Key findings

- Our algorithm reduces the average vertex access {5} close to 1.
- It outperforms BFS in speed on various graph datasets.
- The method effectively leverages shortest path trees for efficiency.

## Abstract

We present a new fast all-pairs shortest path algorithm for unweighted graphs. In breadth-first search which is said to representative and fast in unweighted graphs, the average number of accesses to adjacent vertices (expressed by {\alpha}) is about equal to the average degree of the graph. On the other hand, our algorithm utilizes the shortest path trees of adjacent vertices of each source vertex, and reduce {\alpha} drastically. Roughly speaking {\alpha} is reduced to the value close to 1, because the average degree of a tree is about 2, and one is used to come in and the other is used to go out, although that does not hold true when the depth of the shortest path trees is small. We compared our algorithm with breadth-first search algorithm, and our results showed that ours outperforms breadth-first search on speed and {\alpha}.

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Source: https://tomesphere.com/paper/1908.06806