Universität zu Köln

Fowler, J. Joseph, Gutwenger, Carsten, Jünger, Michael, Mutzel, Petra ORCID: 0000-0001-7621-971X and Schulz, Michael (2009). An SPQR-Tree Approach to Decide Special Cases of Simultaneous Embedding with Fixed Edges. In: Graph Drawing GD 2008, pp. 157-168. Springer-Verlag.

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Abstract

We present a linear-time algorithm for solving the simulta- neous embedding problem with ?xed edges (SEFE) for a planar graph and a pseudoforest (a graph with at most one cycle) by reducing it to the following embedding problem: Given a planar graph G, a cycle C of G, and a partitioning of the remaining vertices of G, does there exist a planar embedding in which the induced subgraph on each vertex partite of G C is contained entirely inside or outside C ? For the latter prob- lem, we present an algorithm that is based on SPQR-trees and has linear running time. We also show how we can employ SPQR-trees to decide SEFE for two planar graphs where one graph has at most two cycles and the intersection is a pseudoforest in linear time. These results give rise to our hope that our SPQR-tree approach might eventually lead to a polynomial-time algorithm for deciding the general SEFE problem for two planar graphs.

Item Type:	Book Section
Creators:	Creators Email ORCID ORCID Put Code Fowler, J. Joseph UNSPECIFIED UNSPECIFIED UNSPECIFIED Gutwenger, Carsten UNSPECIFIED UNSPECIFIED UNSPECIFIED Jünger, Michael UNSPECIFIED UNSPECIFIED UNSPECIFIED Mutzel, Petra UNSPECIFIED https://orcid.org/0000-0001-7621-971X UNSPECIFIED Schulz, Michael UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-549856
Title of Book:	Graph Drawing GD 2008
Series Name:	Lecture notes in computer science
Volume:	5417
Page Range:	pp. 157-168
Date:	2009
Publisher:	Springer-Verlag
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Institute of Computer Science
Subjects:	Data processing Computer science
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/54985