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The Cartographer
An Optimal Algorithm for Product Structure in Planar Graphs
February 17, 2022 Β· Declared Dead Β· π Scandinavian Workshop on Algorithm Theory
"No code URL or promise found in abstract"
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Authors
Prosenjit Bose, Pat Morin, Saeed Odak
arXiv ID
2202.08870
Category
cs.DS: Data Structures & Algorithms
Cross-listed
math.CO
Citations
12
Venue
Scandinavian Workshop on Algorithm Theory
Last Checked
4 months ago
Abstract
The \emph{Product Structure Theorem} for planar graphs (DujmoviΔ et al.\ \emph{JACM}, \textbf{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 $O(n\log n)$ time algorithm (Morin.\ \emph{Algorithmica}, \textbf{85}(5):1544--1558).
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