[{"ddc":["000"],"language":[{"iso":"eng"}],"article_processing_charge":"Yes","project":[{"grant_number":"I05982","name":"Static and Dynamic Hierarchical Graph Decompositions","_id":"bda196b2-d553-11ed-ba76-8e8ee6c21103"}],"scopus_import":"1","department":[{"_id":"MoHe"}],"oa":1,"article_number":"94:1-94:18","publication_identifier":{"isbn":["9783959774451"],"issn":["1868-8969"]},"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","intvolume":"       388","citation":{"ista":"Bhore S, Chang HC, Conroy J, Filtser A, Oh E, Wein N, Zheng DW. 2026. DAG covers for structured graphs: The Steiner point effect. 34th Annual European Symposium on Algorithms. ESA: European Symposium on Algorithms, LIPIcs, vol. 388, 94:1-94:18.","short":"S. Bhore, H.C. Chang, J. Conroy, A. Filtser, E. Oh, N. Wein, D.W. Zheng, in:, 34th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","ama":"Bhore S, Chang HC, Conroy J, et al. DAG covers for structured graphs: The Steiner point effect. In: <i>34th Annual European Symposium on Algorithms</i>. Vol 388. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2026.94\">10.4230/LIPIcs.ESA.2026.94</a>","apa":"Bhore, S., Chang, H. C., Conroy, J., Filtser, A., Oh, E., Wein, N., &#38; Zheng, D. W. (2026). DAG covers for structured graphs: The Steiner point effect. In <i>34th Annual European Symposium on Algorithms</i> (Vol. 388). L’Aquila, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2026.94\">https://doi.org/10.4230/LIPIcs.ESA.2026.94</a>","mla":"Bhore, Sujoy, et al. “DAG Covers for Structured Graphs: The Steiner Point Effect.” <i>34th Annual European Symposium on Algorithms</i>, vol. 388, 94:1-94:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ESA.2026.94\">10.4230/LIPIcs.ESA.2026.94</a>.","ieee":"S. Bhore <i>et al.</i>, “DAG covers for structured graphs: The Steiner point effect,” in <i>34th Annual European Symposium on Algorithms</i>, L’Aquila, Italy, 2026, vol. 388.","chicago":"Bhore, Sujoy, Hsien Chih Chang, Jonathan Conroy, Arnold Filtser, Eunjin Oh, Nicole Wein, and Da Wei Zheng. “DAG Covers for Structured Graphs: The Steiner Point Effect.” In <i>34th Annual European Symposium on Algorithms</i>, Vol. 388. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href=\"https://doi.org/10.4230/LIPIcs.ESA.2026.94\">https://doi.org/10.4230/LIPIcs.ESA.2026.94</a>."},"conference":{"name":"ESA: European Symposium on Algorithms","start_date":"2026-08-31","end_date":"2026-09-04","location":"L’Aquila, Italy"},"oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png"},"corr_author":"1","abstract":[{"lang":"eng","text":"Given a weighted digraph G, a (t,g,μ)-DAG cover is a collection of g dominating DAGs D_1,… ,D_g such that all distances are approximately preserved: for every pair (u,v) of vertices, min_id_{D_i}(u,v) ≤ t⋅ d_G(u,v), and the total number of non-G edges is bounded by |(∪_i D_i)⧵ G| ≤ μ. Assadi, Hoppenworth, and Wein [STOC 25] and Filtser [SODA 26] studied DAG covers for general digraphs. This paper initiates the study of Steiner DAG cover, where the DAGs are allowed to contain Steiner points. \r\nWe obtain Steiner DAG covers on the important classes of planar digraphs and low-treewidth digraphs. Specifically, we show that any digraph with treewidth tw admits a (1,2,Õ(n⋅tw))-Steiner DAG cover. For planar digraphs we provide a (1+ε,2,Õ_ε(n))-Steiner DAG cover.\r\nWe also demonstrate a stark difference between Steiner and non-Steiner DAG covers. As a lower bound, we show that any non-Steiner DAG cover for graphs with treewidth 1 with stretch t < 2 and sub-quadratic number of extra edges requires Ω(log n) DAGs."}],"quality_controlled":"1","volume":388,"acknowledgement":"This work was initiated at Dagstuhl Seminar 25212: Metric Sketching and\r\nDynamic Algorithms for Geometric and Topological Graphs. We thank the organizers and other\r\nparticipants for a productive environment.\r\nujoy Bhore: Work supported in part by ANRF ARG-MATRICS, Grant 002465.\r\nHsien-Chih Chang: Supported by the U.S. National Science Foundation Grant No. CCF-2443017.\r\nJonathan Conroy: Supported by the U.S. National Science Foundation Grant No. CCF-2443017.\r\nArnold Filtser: This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No.\r\n1042/22).\r\nEunjin Oh: Supported by Institute of Information & Communications Technology Planning &\r\nEvaluation (IITP) grant funded by the Korea government (MSIT) (No. RS-2024-00440239, Sublinear\r\nScalable Algorithms for Large-Scale Data Analysis) and the National Research Foundation of Korea\r\n(NRF) grant funded by the Korea government (MSIT) (No. RS-2024-00358505).\r\nNicole Wein: Supported by NSF CAREER award 2541910.\r\nDa Wei Zheng: This project has received funding from the Austrian Science Fund (FWF) grant\r\nDOI 10.55776/I5982. For open access purposes, the author has applied a CC BY public copyright\r\nlicense to any author-accepted manuscript version arising from this submission.","doi":"10.4230/LIPIcs.ESA.2026.94","date_published":"2026-08-25T00:00:00Z","alternative_title":["LIPIcs"],"_id":"22918","year":"2026","status":"public","type":"conference","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Bhore","first_name":"Sujoy","full_name":"Bhore, Sujoy"},{"last_name":"Chang","first_name":"Hsien Chih","full_name":"Chang, Hsien Chih"},{"first_name":"Jonathan","last_name":"Conroy","full_name":"Conroy, Jonathan"},{"full_name":"Filtser, Arnold","last_name":"Filtser","first_name":"Arnold"},{"full_name":"Oh, Eunjin","last_name":"Oh","first_name":"Eunjin"},{"full_name":"Wein, Nicole","first_name":"Nicole","last_name":"Wein"},{"full_name":"Zheng, Da Wei","id":"af77956b-e859-11ef-8dc9-d301b898e32f","first_name":"Da Wei","last_name":"Zheng"}],"day":"25","arxiv":1,"keyword":["Directed graphs","DAG (directed acyclic graphs)","distortion","metric embeddings","planar graph","treewidth"],"file":[{"date_created":"2026-09-17T10:09:22Z","checksum":"2082683b3b72865c6a795305e5d61276","content_type":"application/pdf","file_id":"22948","creator":"dernst","success":1,"access_level":"open_access","relation":"main_file","date_updated":"2026-09-17T10:09:22Z","file_name":"2026_LIPIcsESA_Bhore.pdf","file_size":1123327}],"external_id":{"arxiv":["2604.04186"]},"das_tickbox":"0","OA_type":"gold","publication":"34th Annual European Symposium on Algorithms","date_created":"2026-09-13T22:01:53Z","OA_place":"publisher","has_accepted_license":"1","title":"DAG covers for structured graphs: The Steiner point effect","month":"08","fulldoi":"https://doi.org/10.4230/LIPIcs.ESA.2026.94","supplementarymaterial":"yes","date_updated":"2026-09-17T10:27:46Z","file_date_updated":"2026-09-17T10:09:22Z","researchdata_availability":"no"}]