{"type":"ScholarlyArticle","title":"Taming Treewidth DP with Modulators: A General Booster for Graph Heuristics","authors":[{"name":"Jialiang Li","slug":"jialiang-li","given":"Jialiang","family":"Li","affiliation":""},{"name":"Aneta Neumann","slug":"aneta-neumann","given":"Aneta","family":"Neumann","affiliation":""},{"name":"Frank Neumann","slug":"frank-neumann","given":"Frank","family":"Neumann","affiliation":""},{"name":"Hung Nguyen","slug":"hung-nguyen","given":"Hung","family":"Nguyen","affiliation":""},{"name":"Mingyu Guo","slug":"mingyu-guo","given":"Mingyu","family":"Guo","affiliation":""}],"abstract":"Treewidth is a fundamental graph invariant that quantifies how tree-like\r\na given graph is. It is extensively used with dynamic programming to\r\ndesign fixed-parameter tractable algorithms for many NP-hard graph\r\ncombinatorial optimization problems. However, despite broad theoretical\r\napplicability, treewidth dynamic programming (TDP) does not scale in\r\npractice beyond graphs with very small treewidth. Rather than applying\r\nTDP as a standalone technique, we demonstrate that TDP can serve as a\r\nbroadly applicable enhancer for a wide range of graph combinatorial\r\noptimization algorithms. Our framework leverages the concept of\r\ntreewidth modulators, which refer to vertex sets whose removal\r\nsignificantly reduces the treewidth. We further propose an empirically\r\nefficient procedure for generating such treewidth modulators. To enhance\r\nan algorithm ?, we use ? to heuristically make decisions on the\r\nmodulators vertices, after which the remaining decisions outside the\r\ntreewidth modulators become scalable for TDP.\r\n\r\nTo demonstrate the general applicability of our proposed framework. We\r\nexperimented with three classic graph combinatorial optimization models:\r\nMaximum Independent Set, Minimum Vertex Cover, and Max Cut. We apply TDP\r\nto enhance algorithms across diverse paradigms, including evolutionary\r\nsearch, greedy heuristics, and graph-neural-network-based heuristics.\r\nFor all combinations of optimization models and base algorithms, TDP\r\nsignificantly improves performance over the original methods. In many\r\nsettings, TDP-enhanced greedy heuristics are competitive with, and\r\nsometimes clearly outperform, state-of-the-art commercial solvers.","doi":"10.24963/ijcai.2026/701","url":"https://ijcai.org/proceedings/2026/701","pdf":"https://ijcai.org/proceedings/2026/0701.pdf","markdown":"https://ijcai.org/proceedings/2026/701.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/701","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Search","track":"Main Track","number":701,"pages":{"first":6299,"last":6307},"keywords":["Search: Combinatorial search and optimisation","Search: Search and machine learning","Search: Heuristic search"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}