Academic Journal
DAG Covers for Structured Graphs: The Steiner Point Effect
| Τίτλος: | DAG Covers for Structured Graphs: The Steiner Point Effect |
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| Συγγραφείς: | Bhore, Sujoy, Chang, Hsien-Chih, Conroy, Jonathan, Filtser, Arnold, Oh, Eunjin, Wein, Nicole, Zheng, Da Wei |
| Συνεισφορές: | Sujoy Bhore and Hsien-Chih Chang and Jonathan Conroy and Arnold Filtser and Eunjin Oh and Nicole Wein and Da Wei Zheng |
| Στοιχεία εκδότη: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
| Έτος έκδοσης: | 2026 |
| Συλλογή: | DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) |
| Θεματικοί όροι: | Directed graphs, DAG (directed acyclic graphs), distortion, metric embeddings, planar graph, treewidth |
| Περιγραφή: | 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. |
| Τύπος εγγράφου: | article in journal/newspaper conference object |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| Relation: | Is Part Of LIPIcs, Volume 388, 34th Annual European Symposium on Algorithms (ESA 2026); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2026.94 |
| DOI: | 10.4230/LIPIcs.ESA.2026.94 |
| Διαθεσιμότητα: | https://doi.org/10.4230/LIPIcs.ESA.2026.94 https://nbn-resolving.org/urn:nbn:de:0030-drops-272306 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2026.94 |
| Rights: | https://creativecommons.org/licenses/by/4.0/legalcode |
| Αριθμός Καταχώρησης: | edsbas.ACDC0968 |
| Βάση Δεδομένων: | BASE |
| DOI: | 10.4230/LIPIcs.ESA.2026.94 |
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