Problem Reductions at Scale: Agentic Integration of Computationally Hard Problems

2026-04-13

AI Summary

This work addresses the lack of scalable, general-purpose tools for polynomial-time reductions among NP-hard optimization problems, which hinders flexible integration with quantum hardware, commercial solvers, or heuristic algorithms. The authors propose a "constraint engineering" framework that leverages AI-powered coding agents to automatically construct a comprehensive reduction library. Built in Rust, the system features type safety, multi-layer verification, and a fully automated pipeline for implementation, review, and integration, enabling composable, transitive reduction graphs. Within three months, the team developed over 170,000 lines of code, covering more than 100 NP-hard problems and 200 reduction rules. Once a new solver is registered, it immediately becomes available across the entire connected component of the reduction graph, significantly enhancing reusability and interoperability.

Technology Category

• Constraint Satisfaction and Optimization: Solvers and Tools
• Search and Optimization: Combinatorial Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

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.

Problem

• NP-hard
• problem reduction
• optimization
• solver interoperability
• computational complexity

Innovation

• harness engineering
• problem reductions
• AI coding agents
• NP-hard optimization
• automated software integration