# Breaking the Sorting Barrier for Directed Single-Source Shortest Paths

arXiv: https://arxiv.org/abs/2504.17033 · HTML: https://mlsanity.com/paper/2504.17033/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2025.

## Built on by (most cited first, 1 of 1)

- [Physical Transformer](https://mlsanity.com/paper/2601.02433/) (2026)

## Abstract (arXiv)

We give a deterministic O(mlog2/3n)-time algorithm for single-source shortest paths (SSSP) on directed graphs with real non-negative edge weights in the comparison-addition model. This is the first result to break the O(m+nlog n) time bound of Dijkstra's algorithm on sparse graphs, showing that Dijkstra's algorithm is not optimal for SSSP.