# Problem Reductions at Scale: Agentic Integration of Computationally Hard Problems

arXiv: https://arxiv.org/abs/2604.11535 · HTML: https://mlsanity.com/paper/2604.11535/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Software engineering coding agents, one of 16 directions in LLM agents and tool use.
- Builds on 18 of its 63 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Placed in

- LLM agents and tool use / [Software engineering coding agents](https://mlsanity.com/agents/software-engineering-coding-agents/)

## Builds on (most cited first, 18 of 18)

- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [OpenHands: An Open Platform for AI Software Developers as Generalist Agents](https://mlsanity.com/paper/2407.16741/) (2024)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Humanity's Last Exam](https://mlsanity.com/paper/2501.14249/) (2025)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [SWE-Bench Pro: Can AI Agents Solve Long-Horizon Software Engineering Tasks?](https://mlsanity.com/paper/2509.16941/) (2025)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2107.01188/) (2021)
- [Measuring the Impact of Early-2025 AI on Experienced Open-Source Developer Productivity](https://mlsanity.com/paper/2507.09089/) (2025)
- [Live-SWE-agent: Can Software Engineering Agents Self-Evolve on the Fly?](https://mlsanity.com/paper/2511.13646/) (2025)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [SWE-EVO: Benchmarking Coding Agents in Long-Horizon Software Evolution Scenarios](https://mlsanity.com/paper/2512.18470/) (2025)
- [LongCLI-Bench: A Preliminary Benchmark and Study for Long-horizon Agentic Programming in Command-Line Interfaces](https://mlsanity.com/paper/2602.14337/) (2026)
- [Exact Algorithms for Maximum Independent Set](https://mlsanity.com/paper/1312.6260/) (2013)
- [QUBO.jl: A Julia Ecosystem for Quadratic Unconstrained Binary Optimization](https://mlsanity.com/paper/2307.02577/) (2023)

## Abstract (arXiv)

Solving an NP-hard optimization problem often requires reformulating it for a specific solver -- quantum hardware, a commercial optimizer, or a domain heuristic. A tool for polynomial-time reductions between hard problems would let practitioners route any supported problem to any supported solver through a single interface. Building such a library at scale, however, has remained out of reach. We show that harness engineering, the practice of designing constraints, verification systems, and feedback loops that channel AI coding agents, can overcome this barrier. Our harness combines a no-code contribution route for domain experts, a multilayer verification stack ranging from type-level checks to agentic feature tests (AI agents role-playing as end users), and a fully automated implementation-review-integration pipeline. In about three months, we built a command-line tool backed by a library of 100+ problem types and 200+ reduction rules in over 170k lines of Rust. The result suggests that a well-engineered harness lets agents build well-tested software at a scale and pace beyond prior reduction-library efforts. Because the reduction graph composes transitively, a new solver registered for any single problem type instantly becomes available to every problem connected by a reduction path. The source code is available at https://github.com/CodingThrust/problem-reductions.