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

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

Authors: Frati, Fabrizio

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.


Source : oai:HAL:hal-00990461v1
Volume: Vol. 12 no. 5
Section: Graph and Algorithms
Published on: January 1, 2010
Submitted 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]


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