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DAG Covers for Structured Graphs: The Steiner Point Effect

Authors Sujoy Bhore , Hsien-Chih Chang , Jonathan Conroy , Arnold Filtser , Eunjin Oh , Nicole Wein , Da Wei Zheng

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Graph algorithms analysis
Keywords
  • Directed graphs
  • DAG (directed acyclic graphs)
  • distortion
  • metric embeddings
  • planar graph
  • treewidth

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Abstract

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. 
We 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.
We 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.

Cite As Get BibTex

Sujoy Bhore, 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 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 94:1-94:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.94

Author Details

Sujoy Bhore
  • Indian Institute of Technology Bombay, India
Hsien-Chih Chang
  • Dartmouth College, Hanover, NH, USA
Jonathan Conroy
  • Dartmouth College, Hanover, NH, USA
Arnold Filtser
  • Bar-Ilan University, Ramat Gan, Israel
Eunjin Oh
  • POSTECH, Pohang, South Korea
Nicole Wein
  • University of Michigan, Ann Arbor, MI, USA
Da Wei Zheng
  • Institute of Science and Technology Austria, Klosterneuburg, Austria

Funding

  • Bhore, Sujoy: Work supported in part by ANRF ARG-MATRICS, Grant 002465.
  • Chang, Hsien-Chih: Supported by the U.S. National Science Foundation Grant No. CCF-2443017.
  • Conroy, Jonathan: Supported by the U.S. National Science Foundation Grant No. CCF-2443017.
  • Filtser, Arnold: This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 1042/22).
  • Oh, Eunjin: Supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. RS-2024-00440239, Sublinear Scalable Algorithms for Large-Scale Data Analysis) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2024-00358505).
  • Wein, Nicole: Supported by NSF CAREER award 2541910.
  • Zheng, Da Wei: This project has received funding from the Austrian Science Fund (FWF) grant https://www.doi.org/10.55776/I5982. For open access purposes, the author has applied a CC BY public copyright license to any author-accepted manuscript version arising from this submission.

Acknowledgements

This work was initiated at Dagstuhl Seminar 25212: Metric Sketching and Dynamic Algorithms for Geometric and Topological Graphs. We thank the organizers and other participants for a productive environment.

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