OptimShortestPaths.jl

Transform optimization problems into graph shortest paths using the efficient DMY algorithm

Overview

OptimShortestPaths is a Julia package that provides a unified framework for solving optimization problems by transforming them into shortest-path problems on directed graphs. The package implements the state-of-the-art DMY (Duan-Mao-Yin) algorithm from STOC 2025, achieving O(m log^(2/3) n) time complexity for single-source shortest paths.

Key Features

• Efficient Algorithm: DMY algorithm with O(m log^(2/3) n) complexity
• Multi-Objective: Pareto front computation with bounded solutions
• Domain-Agnostic: Transform ANY optimization problem to shortest paths
• Domain-Specific: Built-in support for drug discovery, metabolic networks, treatment protocols
• Well-Tested: 1,700+ assertions across algorithm, domain, and documentation coverage
• Publication-Quality: Professional figures and comprehensive benchmarks

Quick Start

using Pkg
Pkg.add("OptimShortestPaths")
using OptimShortestPaths

# Create a graph
edges = [Edge(1, 2, 1), Edge(2, 3, 2), Edge(1, 3, 3)]
weights = [1.0, 2.0, 4.0]
graph = DMYGraph(3, edges, weights)

# Run DMY algorithm
distances = dmy_sssp!(graph, 1)  # Source vertex 1
println("Distances: ", distances)  # [0.0, 1.0, 3.0]

Cheat Sheet

• For a comprehensive, example-driven overview, see the Cheat Sheet page. It includes:
  • Core shortest-path usage with line-by-line annotations
  • Utilities, validations, and analysis helpers
  • Multi-objective strategies and topology diagrams
  • A categorized function reference and detailed output-key tables

Installation

The package requires Julia 1.9 or later:

using Pkg
Pkg.add("OptimShortestPaths")

For development version:

using Pkg
Pkg.develop("OptimShortestPaths")

Core Concepts

Problem Transformation Philosophy

OptimShortestPaths transforms optimization problems into shortest-path problems:

1. Entities → Vertices: Map domain objects to graph vertices
2. Relationships → Edges: Convert interactions/transitions to directed edges
3. Objectives → Weights: Transform costs to non-negative edge weights
4. Solutions → Paths: Shortest paths = optimal solutions

Why This Approach?

• Unified Framework: One algorithm solves many problems
• Efficient: O(m log^(2/3) n) complexity beats many domain-specific methods
• Flexible: Generic graph utilities work for any domain
• Proven: Based on award-winning STOC 2025 algorithm

Main Components

Core Algorithm

• dmy_sssp! - Main DMY shortest path algorithm
• DMYGraph - Graph data structure
• bmssp! - Bounded Multi-Source Shortest Path subroutine

Multi-Objective Optimization

• compute_pareto_front - Pareto front computation
• weighted_sum_approach - Scalarization method
• epsilon_constraint_approach - ε-constraint method

Domain Applications

• Drug-target network analysis
• Metabolic pathway optimization
• Treatment protocol sequencing
• Supply chain optimization

Performance

Benchmarks on sparse random graphs (m ≈ 2n):

DMY becomes faster than Dijkstra at approximately n ≈ 1,800 vertices.

Citation

If you use OptimShortestPaths in your research, please cite:

@software{optimshortestpaths2025,
  title = {OptimShortestPaths: Optimization via Shortest Paths},
  author = {Tianchi Chen},
  year = {2025},
  url = {https://github.com/danielchen26/OptimShortestPaths.jl}
}

@inproceedings{dmy2025,
  title = {Breaking the Dijkstra Barrier for Directed Single-Source Shortest-Paths via Structured Distances},
  author = {Duan, Ran and Mao, Jiawei and Yin, Hao and Zhou, Hengming},
  booktitle = {Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC 2025)},
  year = {2025},
  note = {Best Paper Award}
}

Contributing

Contributions are welcome! Please:

• Add tests for new features
• Update benchmarks with your hardware specs
• Cite relevant papers for algorithmic contributions
• Follow Julia style guidelines

License

MIT License - see LICENSE file for details.

Acknowledgments

The DMY algorithm implementation is based on the STOC 2025 Best Paper by Duan, Mao, Yin, and Zhou.