智能体算法工程：改进共享内存精确最小割
Agentic Algorithm Engineering: Improving Shared-Memory Exact Minimum Cuts
- New Jersey Institute of Technology（新泽西理工学院）
- Heidelberg University（海德堡大学）
- Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文引入智能体算法工程（AAE）方法，利用自主大语言模型智能体自动优化共享内存精确最小割算法，在真实和DIMACS实例上获得显著加速。
AI中文摘要：
无向边加权图的最小割问题要求我们将节点集划分为两个块，同时最小化割边的加权和。在过去几年中，我们针对该问题设计了一系列快速算法。我们最快的精确算法使用一种非精确算法来获得更好的问题下界，依赖于该下界的归约、改进的数据结构以及并行收缩例程。该算法已在开源软件包VieCut中提供，在真实世界实例上，顺序执行时比先前最快的求解器快最多2.5倍，并行执行时快最多12.9倍。我们使用智能体算法工程（AAE）改进了该算法，AAE是我们在此引入的一种方法论，其中自主的大语言模型智能体在现有代码库上运行算法工程循环：它们形成关于运行时间损失所在的假设，实现这些假设，在固定实例集上对结果进行基准测试，并保留或丢弃更改。尽管我们已经对手动调整算法进行了广泛优化，智能体仍发现了显著的优化，特别是在DIMACS核心实例上：在真实世界k-核上，顺序执行和32线程并行的加速比分别为1.28和1.63，在DIMACS核心实例上分别为6.26和127。
英文摘要：
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weighted sum of the cut edges. Over the last years, we engineered a range of fast algorithms for this problem. Our fastest exact algorithm uses an inexact algorithm to obtain a better bound for the problem, reductions that depend on this bound, improved data structures and parallel contraction routines. It is available in the open-source package VieCut and, on real-world instances, outperformed the previously fastest solvers by a factor of up to 2.5 sequentially and up to 12.9 when run in parallel. We improve this algorithm using agentic algorithm engineering (AAE), a methodology that we introduce here, in which autonomous large language model agents run the algorithm engineering cycle on an existing code base: they form hypotheses about where running time is lost, implement them, benchmark the result on a fixed instance set and keep or discard the change. Even though we had already tuned our algorithm by hand extensively, the agent finds significant optimizations, in particular on the DIMACS core instances: factors of 1.28 (sequential) and 1.63 (32 threads) on real-world k-cores, and 6.26 and 127 on the DIMACS core instances.
