{"arxiv":1,"_id":"21140","publication":"Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms","department":[{"_id":"VlKo"}],"date_created":"2026-02-05T10:51:34Z","oa":1,"conference":{"location":"Vancouver, Canada","end_date":"2026-01-14","name":"SODA: Symposium on Discrete Algorithms","start_date":"2026-01-11"},"month":"01","external_id":{"arxiv":["2409.20314"]},"status":"public","quality_controlled":"1","abstract":[{"lang":"eng","text":"We consider several problems related to packing forests in graphs. The first one is to find k edge-disjoint forests in a directed graph G of maximal size such that the indegree of each vertex in these forests is at most k. We describe a min-max characterization for this problem and show that it can be solved in almost linear time for fixed k, extending the algorithm of [Gabow, 1995]. Specifically, the complexity is O(kδm log n), where n, m are the number of vertices and edges in G respectively, and δ = max{1, k − kG}, where kG is the edge connectivity of the graph. Using our solution to this problem, we improve complexities for two existing applications:(1) k-forest problem: find k forests in an undirected graph G maximizing the number of edges in their union. We show how to solve this problem in O(k3 min{kn, m} log2 n + k · MAXFLOW(m, m) log n) time, breaking the Ok(n3/2) complexity barrier of previously known approaches.(2) Directed edge-connectivity augmentation problem: find a smallest set of directed edges whose addition to the given directed graph makes it strongly k-connected. We improve the deterministic complexity for this problem from O(kδ(m + δn) log n) [Gabow, STOC 1994] to O(kδm log n). A similar approach with the same complexity also works for the undirected version of the problem."}],"OA_type":"green","page":"4023-4042","date_updated":"2026-02-16T09:18:33Z","citation":{"ista":"Arkhipov P, Kolmogorov V. 2026. Faster algorithms for packing forests in graphs and related problems. Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms, 4023–4042.","chicago":"Arkhipov, Pavel, and Vladimir Kolmogorov. “Faster Algorithms for Packing Forests in Graphs and Related Problems.” In <i>Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, 4023–42. Society for Industrial and Applied Mathematics, 2026. <a href=\"https://doi.org/10.1137/1.9781611978971.148\">https://doi.org/10.1137/1.9781611978971.148</a>.","ieee":"P. Arkhipov and V. Kolmogorov, “Faster algorithms for packing forests in graphs and related problems,” in <i>Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Vancouver, Canada, 2026, pp. 4023–4042.","ama":"Arkhipov P, Kolmogorov V. Faster algorithms for packing forests in graphs and related problems. In: <i>Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms</i>. Society for Industrial and Applied Mathematics; 2026:4023-4042. doi:<a href=\"https://doi.org/10.1137/1.9781611978971.148\">10.1137/1.9781611978971.148</a>","apa":"Arkhipov, P., &#38; Kolmogorov, V. (2026). Faster algorithms for packing forests in graphs and related problems. In <i>Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms</i> (pp. 4023–4042). Vancouver, Canada: Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/1.9781611978971.148\">https://doi.org/10.1137/1.9781611978971.148</a>","short":"P. Arkhipov, V. Kolmogorov, in:, Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, 2026, pp. 4023–4042.","mla":"Arkhipov, Pavel, and Vladimir Kolmogorov. “Faster Algorithms for Packing Forests in Graphs and Related Problems.” <i>Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms</i>, Society for Industrial and Applied Mathematics, 2026, pp. 4023–42, doi:<a href=\"https://doi.org/10.1137/1.9781611978971.148\">10.1137/1.9781611978971.148</a>."},"author":[{"full_name":"Arkhipov, Pavel","first_name":"Pavel","id":"b25f2ab2-1fed-11ee-8599-fe02d211784f","last_name":"Arkhipov"},{"first_name":"Vladimir","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","type":"conference","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2409.20314"}],"OA_place":"repository","language":[{"iso":"eng"}],"corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Society for Industrial and Applied Mathematics","doi":"10.1137/1.9781611978971.148","year":"2026","date_published":"2026-01-07T00:00:00Z","day":"07","oa_version":"Preprint","title":"Faster algorithms for packing forests in graphs and related problems","article_processing_charge":"No","publication_identifier":{"eisbn":["9781611978971"]}}