Fabrizio Frati - Lower Bounds on the Area Requirements of Series-Parallel Graphs

dmtcs:500 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 5 - https://doi.org/10.46298/dmtcs.500
Lower Bounds on the Area Requirements of Series-Parallel Graphs

Authors: Fabrizio Frati ORCID-iD1,2

We show that there exist series-parallel graphs requiring Omega(n2(root log n)) area in any straight-line or poly-line grid drawing. Such a result is achieved in two steps. First, we show that, in any straight-line or poly-line drawing of K(2,n), one side of the bounding box has length Omega(n), thus answering two questions posed by Biedl et al. Second, we show a family of series-parallel graphs requiring Omega(2(root log n)) width and Omega(2(root log n)) height in any straight-line or poly-line grid drawing. Combining the two results, the Omega(n2(root log n)) area lower bound is achieved.

Volume: Vol. 12 no. 5
Section: Graph and Algorithms
Published on: January 1, 2010
Imported on: March 26, 2015
Keywords: planar graphs,series-parallel graphs,area requirements,graph drawing,straight-line drawings,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV 1610.02841
Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.jcss.2019.08.001
Source : ScholeXplorer IsRelatedTo DOI 10.1137/1.9781611974782.129
Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1610.02841
Source : ScholeXplorer IsRelatedTo HANDLE 11590/360767
  • 10.48550/arxiv.1610.02841
  • 11590/360767
  • 10.1016/j.jcss.2019.08.001
  • 10.1016/j.jcss.2019.08.001
  • 1610.02841
  • 10.1137/1.9781611974782.129
  • 10.1137/1.9781611974782.129
LR-drawings of ordered rooted binary trees and near-linear area drawings of outerplanar graphs

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