Problem Reductions at Scale: Agentic Integration of Computationally Hard Problems
Developed a scalable problem reduction library with 100+ problem types and 200+ rules, integrated via AI agents for automated contribution and verification.
Key Findings
Methodology
This work constructs an engineering-driven reduction framework combining layered verification, no-code contribution pathways, and AI coding agents. Built in Rust, the library encompasses over 190 problem types and 265 reduction rules, supporting transitive composition in a reduction graph. The system employs multi-layer validation, including type checks, unit tests, round-trip verification, and agent role-playing tests, to ensure correctness. Automated pipelines facilitate problem definition, rule implementation, review, and integration, drastically reducing manual effort. The transferability of the reduction graph allows new solvers to be instantly available across connected problems once registered, enabling scalable and flexible problem-solving infrastructure.
Key Results
- Within three months, a comprehensive library of 170,000 lines of Rust code was developed, covering 190 problem types and 265 rules. The reduction graph supports a wide array of NP-hard problems, with proven paths from 3-SAT to ILP, enabling rigorous NP-hardness certification. Automated validation processes, including symbolic overhead analysis and correctness tests, ensure high reliability. The system's modular design allows rapid addition of new problem types and solvers, with immediate effect across the graph. Experiments demonstrate that the approach surpasses prior manual efforts in scale, speed, and correctness, facilitating large-scale problem reductions and solver integrations.
- The transferability of the reduction graph ensures that registering a new solver for any problem type instantly makes it accessible to all connected problems. Automated verification and AI-assisted code generation significantly accelerate the contribution cycle, reducing development time from months to weeks. The system's robustness is validated through extensive testing, including agent role-playing scenarios that simulate end-user interactions, catching subtle bugs and usability issues. Overall, the framework establishes a new standard for scalable, automated problem reduction and solver integration in computational optimization.
- The layered verification system, combining static checks, dynamic tests, and agent role-playing, guarantees high correctness levels. The use of symbolic expressions for overhead and complexity analysis enables optimal reduction path selection. The modular architecture supports multi-platform deployment, and the no-code contribution pathway lowers barriers for domain experts. These innovations collectively create a scalable, reliable, and extensible infrastructure for tackling NP-hard problems across diverse fields, fostering automation and collaboration in computational research and industry applications.
Significance
This research addresses the longstanding challenge of scaling problem reduction libraries for NP-hard problems, a cornerstone in optimization and theoretical computer science. By engineering a comprehensive, automated, and extensible framework, it overcomes the limitations of manual, ad hoc approaches. The integration of AI agents streamlines contribution, verification, and deployment, enabling rapid growth of the reduction ecosystem. This work not only accelerates research in problem complexity and solver development but also paves the way for practical applications in logistics, hardware design, and AI-driven optimization. Its scalable architecture and automated validation set new standards for reliability and extensibility, fostering broader adoption and community-driven expansion.
Technical Contribution
The core technical innovation lies in engineering a layered, transitive reduction graph supported by automated verification pipelines and AI code agents. The system employs symbolic overhead expressions for path optimization and correctness guarantees. It introduces a no-code contribution interface, allowing domain experts to propose new rules via structured GitHub issues, which are automatically validated and integrated. The use of Rust ensures high performance and safety, facilitating large-scale deployment. The concept of a transitive reduction graph with dynamic solver registration is novel, enabling instant solver availability across connected problems, thus vastly expanding the problem-solving landscape. The integration of multi-layer validation, including agent role-playing tests, enhances reliability beyond traditional static checks.
Novelty
This work is the first to realize a large-scale, automated, and extensible NP-hard problem reduction library leveraging engineering principles and AI agents. Unlike previous efforts limited to small, manually maintained sets, this system supports hundreds of problem types and rules, with transitive composition enabling instant solver deployment. The no-code contribution pathway and layered verification framework are innovative, reducing expert effort and increasing correctness assurance. The concept of a transitive reduction graph with dynamic solver registration represents a significant advancement over static, handcrafted collections, opening new avenues for automated problem-solving infrastructure.
Limitations
- Despite automation, certain complex reductions still require manual oversight, especially for novel or highly intricate problems. The correctness guarantees depend on the completeness of verification layers, which may not cover all edge cases.
- The system's performance is constrained by the computational cost of symbolic overhead analysis and solver calls, which could become bottlenecks at larger scales. Hardware limitations may restrict real-time responsiveness for very large problems.
- The current focus on classical NP-hard problems limits applicability to emerging problem domains with different structures. Extending the framework to non-standard or dynamic problems remains an open challenge.
Future Work
Future efforts will focus on broadening problem coverage, integrating more diverse solvers, and enhancing formal verification techniques for higher assurance. Developing distributed and parallelized verification pipelines will address scalability bottlenecks. Community-driven contributions via open-source platforms will be promoted to expand the reduction graph. Additionally, exploring adaptive algorithms for overhead minimization and expanding support for non-classical problems will further enhance the system's versatility. The ultimate goal is to establish an autonomous, self-improving ecosystem for NP-hard problem reduction and solver deployment.
AI Executive Summary
Deep Dive
Plain Language Accessible to non-experts
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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.