The Product Structure Theorem for planar graphs (Dujmović et al. JACM, 67(4):22) states that any planar graph is contained in the strong product of a planar 3-tree, a path, and a 3-cycle. We give a simple linear-time algorithm for finding this decomposition as well as several related decompositions. This improves on the previous O(nlog n) time algorithm (Morin. Algorithmica, 85(5):1544-1558).
@InProceedings{bose_et_al:LIPIcs.SWAT.2022.19, author = {Bose, Prosenjit and Morin, Pat and Odak, Saeed}, title = {{An Optimal Algorithm for Product Structure in Planar Graphs}}, booktitle = {18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)}, pages = {19:1--19:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-236-5}, ISSN = {1868-8969}, year = {2022}, volume = {227}, editor = {Czumaj, Artur and Xin, Qin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.19}, URN = {urn:nbn:de:0030-drops-161797}, doi = {10.4230/LIPIcs.SWAT.2022.19}, annote = {Keywords: Planar graphs, product structure} }
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