Deepening the Relationship between SEFE and C-Planarity
Computational Complexity
2014-04-25 v1 Data Structures and Algorithms
Abstract
In this paper we deepen the understanding of the connection between two long-standing Graph Drawing open problems, that is, Simultaneous Embedding with Fixed Edges (SEFE) and Clustered Planarity (C-PLANARITY). In his GD'12 paper Marcus Schaefer presented a reduction from C-PLANARITY to SEFE of two planar graphs (SEFE-2). We prove that a reduction exists also in the opposite direction, if we consider instances of SEFE-2 in which the intersection graph is connected. We pose as an open question whether the two problems are polynomial-time equivalent.
Cite
@article{arxiv.1404.6175,
title = {Deepening the Relationship between SEFE and C-Planarity},
author = {Patrizio Angelini and Giordano Da Lozzo},
journal= {arXiv preprint arXiv:1404.6175},
year = {2014}
}
Comments
8 pages, 3 figures, Extended version of 'SEFE = C-Planarity?' (9th International Colloquium on Graph Theory and Combinatorics - ICGT 2014)