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

**Authors:** Ran Duan, Jiayi Mao, Xiao Mao, Xinkai Shu, Longhui Yin  
**arXiv:** [2504.17033](https://arxiv.org/abs/2504.17033)  
**Date:** 2025-04-23  
**Summary page:** https://www.summarizepaper.com/en/paper/2504.17033v2/

## Key points

- Authors present a deterministic algorithm for solving single-source shortest paths (SSSP) problem on directed graphs with real non-negative edge weights in the comparison-addition model.
- The algorithm achieves a time complexity of $O(m\log^{2/3}n)$, significantly improving upon the previous best-known bound of $O(m+n\log n)$ set by Dijkstra's algorithm on sparse graphs.
- The paper addresses limitations of existing algorithms and paves the way for further research into optimizing SSSP computations on directed graphs.
- This breakthrough result has implications beyond theoretical computer science, opening up new possibilities for more efficient algorithms in practical applications where SSSP computations are crucial.
- The work showcases the potential for further advancements in solving SSSP problems with real non-negative edge weights, breaking through a long-standing time barrier.

## Summary

In their paper titled "Breaking the Sorting Barrier for Directed Single-Source Shortest Paths," authors Ran Duan, Jiayi Mao, Xiao Mao, Xinkai Shu, and Longhui Yin present a groundbreaking deterministic algorithm for solving the single-source shortest paths (SSSP) problem on directed graphs with real non-negative edge weights in the comparison-addition model. This innovative approach to tackling a fundamental problem in graph theory marks a significant advancement in algorithm design and analysis. are crucial in many practical applications. The authors' work  on the limitations of existing algorithms and paves the way for further research into optimizing SSSP computations on directed graphs. By achieving a time complexity of $O(m\log^{2/3}n)$, this algorithm significantly improves upon the previous best-known bound of $O(m+n\log n)$ set by Dijkstra's algorithm on sparse graphs. Through their breakthrough result, the authors demonstrate that  for solving SSSP in certain scenarios. This has implications beyond theoretical computer science as it opens up new possibilities for more efficient algorithms in practical applications where SSSP computations are crucial. with real non-negative edge weights pose unique challenges when it comes to solving SSSP problems. However, this paper presents an innovative solution that breaks through a long-standing time barrier and showcases the potential for further advancements in this field. In conclusion, this paper highlights the importance of constantly pushing boundaries and exploring new approaches to solve fundamental problems such as . The authors' work serves as an inspiration for future research and advancements in algorithm design and analysis.