AI 中文总结
该研究提出基于树宽调制器的框架，用树宽动态规划增强各类图组合优化算法，在三类模型和多种范式算法上均显著提升性能，部分贪心算法表现优于商用求解器。
AI 中文摘要
树宽是衡量图与树相似程度的基础图不变量，被广泛结合动态规划设计针对众多NP困难图组合优化问题的固定参数可处理算法。然而，尽管树宽动态规划（TDP）具有广泛的理论适用性，但在树宽极小的图之外，TDP在实际应用中无法扩展。本文不将TDP作为独立技术使用，而是证明其可作为广泛适用的增强器，用于各类图组合优化算法。我们的框架利用树宽调制器的概念，即移除后能大幅降低树宽的顶点集；还提出了一种经验上高效的树宽调制器生成流程。为增强算法A，我们用A对调制器顶点做出启发式决策，之后树宽调制器外的剩余决策可通过TDP高效处理。为验证框架的通用性，我们在三个经典图组合优化模型（最大独立集、最小顶点覆盖、最大割）上进行实验，将TDP用于增强不同范式的算法，包括进化搜索、贪心启发式算法、基于图神经网络的启发式算法。对于所有优化模型与基础算法的组合，TDP均显著提升了原始方法的性能；在诸多场景下，经TDP增强的贪心启发式算法可与最先进的商用求解器相媲美，有时甚至明显优于后者。
英文摘要
Treewidth is a fundamental graph invariant that quantifies how tree-like a given graph is. It is extensively used with dynamic programming to design fixed-parameter tractable algorithms for many NP-hard graph combinatorial optimization problems. However, despite broad theoretical applicability, treewidth dynamic programming (TDP) does not scale in practice beyond graphs with very small treewidth. Rather than applying TDP as a standalone technique, in this paper, we demonstrate that TDP can serve as a broadly applicable enhancer for a wide range of graph combinatorial optimization algorithms. Our framework leverages the concept of treewidth modulators, which refer to vertex sets whose removal significantly reduces the treewidth. We further propose an empirically efficient procedure for generating such treewidth modulators. To enhance an algorithm $\textit{A}$, we use $\textit{A}$ to heuristically make decisions on the modulators vertices, after which the remaining decisions outside the treewidth modulators become scalable for TDP. To demonstrate the general applicability of our proposed framework. We experimented with three classic graph combinatorial optimization models: Maximum Independent Set, Minimum Vertex Cover, and Max Cut. We apply TDP to enhance algorithms across diverse paradigms, including evolutionary search, greedy heuristics, and graph-neural-network-based heuristics. For all combinations of optimization models and base algorithms, TDP significantly improves performance over the original methods. In many settings, TDP-enhanced greedy heuristics are competitive with, and sometimes clearly outperform, state-of-the-art commercial solvers.
CommentsAccepted for publication in the Proceedings of IJCAI 2026
Journal refProceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence (IJCAI-26), Main Track, pp. 6299-6307, 2026
