{"type":"ScholarlyArticle","title":"Efficient Parallel Algorithms with Linear Queries for Non-Monotone Submodular Maximization","authors":[{"name":"Canh V. Pham","slug":"canh-v-pham","given":"Canh V.","family":"Pham","affiliation":""},{"name":"Tan D. Tran","slug":"tan-d-tran","given":"Tan D.","family":"Tran","affiliation":""},{"name":"Dung T. K. Ha","slug":"dung-t-k-ha","given":"Dung T.K.","family":"Ha","affiliation":""},{"name":"My T. Thai","slug":"my-t-thai","given":"My T.","family":"Thai","affiliation":""}],"abstract":"In this work, we propose the first constant-approximation algorithms,\r\nLinAst and LinAtg, which simultaneously achieve optimal\r\nquery complexity O(n) and adaptive complexity O(log n) for non-monotone\r\nsubmodular maximization under a cardinality constraint k over a ground set of\r\nsize n. Specifically, compared with existing algorithms that attain the best\r\nknown adaptive complexity of O(log n), our approach preserves this adaptivity\r\nwhile reducing the query complexity from O(n log k) to O(n) and improving\r\nthe approximation ratio from 0.172-epsilon to 0.193-epsilon.\r\nOur algorithms are built upon LinAdapt, which achieves a constant\r\napproximation ratio with O(log n) adaptive rounds and linear query\r\ncomplexity by requiring only O(1) candidate guesses of the optimal value.\r\nWe further introduce the BoostAdapt algorithm, which improves the\r\napproximation guarantee to 0.25-\\epsilon with O(log n log k) adaptive\r\ncomplexity and O(n log k) query complexity, based on a novel staggered greedy\r\nthreshold framework that alternately constructs two disjoint solution sets over\r\nO(log k) sequential rounds. Extensive experiments on standard benchmark\r\ndatasets demonstrate that our algorithms consistently outperform\r\nstate-of-the-art methods in terms of solution quality, query complexity, and running time.","doi":"10.24963/ijcai.2026/259","url":"https://ijcai.org/proceedings/2026/259","pdf":"https://ijcai.org/proceedings/2026/0259.pdf","markdown":"https://ijcai.org/proceedings/2026/259.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/259","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":"Constraint Satisfaction and Optimization","track":"Main Track","number":259,"pages":{"first":2328,"last":2336},"keywords":["Constraint Satisfaction and Optimization: Constraint optimization problems","Machine Learning: Optimization","Constraint Satisfaction and Optimization: Constraint satisfaction","Machine Learning: Theory of deep learning"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}