Results 11 to 20 of about 157,734 (242)

Atomic Embeddability, Clustered Planarity, and Thickenability [PDF]

Journal of the ACM, 2020
We study the atomic embeddability testing problem, which is a common generalization of clustered planarity ( c-planarity , for short) and thickenability testing, and present a polynomial-time algorithm for this problem, thereby giving the first polynomial-time algorithm for c-planarity.
Radoslav Fulek, Csaba D. Tóth
openaire   +7 more sources

Clustered Planarity Variants for Level Graphs [PDF]

CoRR
We consider variants of the clustered planarity problem for level-planar drawings. So far, only convex clusters have been studied in this setting. We introduce two new variants that both insist on a level-planar drawing of the input graph but relax the requirements on the shape of the clusters.
Simon D. Fink, Matthias Pfretzschner, Ignaz Rutter, Marie Diana Sieper   +3 more
core   +7 more sources

Shrinking the Search Space for Clustered Planarity [PDF]

, 2013
A clustered graph is a graph augmented with a hierarchical inclusion structure over its vertices, and arises very naturally in multiple application areas. While it is long known that planarity--i.e., drawability without edge crossings--of graphs can be tested in polynomial (linear) time, the complexity for the clustered case is still unknown.
Markus Chimani, Karsten Klein 0001
core   +3 more sources

Clustered Planarity: Small Clusters in Eulerian Graphs [PDF]

, 2008
We present several polynomial-time algorithms for c-planarity testing for clustered graphs with clusters of size at most three. The most general result concerns a special class of Eulerian graphs, namely graphs obtained froma fixed-size 3-connected graph bymultiplying and then subdividing edges.
Eva Jelínková, Jan Kára, Jan Kratochvíl, Martin Pergel, Ondrej Suchý 0001, Tomás Vyskocil   +5 more
openaire   +3 more sources

NodeTrix Planarity Testing with Small Clusters [PDF]

Algorithmica, 2018
We study the NodeTrix planarity testing problem for flat clustered graphs when the maximum size of each cluster is bounded by a constant $k$. We consider both the case when the sides of the matrices to which the edges are incident are fixed and the case when they can be chosen arbitrarily. We show that NodeTrix planarity testing with fixed sides can be
Di Giacomo E., Liotta G., Patrignani M., Rutter I., Tappini A.   +4 more
core   +9 more sources

Splitting Clusters to Get C-Planarity [PDF]

, 2010
In this paper we introduce a generalization of the c-planarity testing problem for clustered graphs. Namely, given a clustered graph, the goal of the Split-C-Planarity problem is to split as few clusters as possible in order to make the graph c-planar. Determining whether zero splits are enough coincides with testing c-planarity.
Patrizio Angelini, Fabrizio Frati, Maurizio Patrignani   +2 more
openaire   +4 more sources

Constrained Planarity in Practice -- Engineering the Synchronized Planarity Algorithm [PDF]

Journal of Graph Algorithms and Applications
In the constrained planarity setting, we ask whether a graph admits a planar drawing that additionally satisfies a given set of constraints. These constraints are often derived from very natural problems; prominent examples are Level Planarity, where ...
Simon Dominik Fink, Ignaz Rutter
doaj   +3 more sources

Exact Algorithms for Clustered Planarity with Linear Saturators [PDF]

CoRR
Bibliografija: str. 14-16.
Giordano Da Lozzo, Robert Ganian, Siddharth Gupta 0002, Bojan Mohar, Sebastian Ordyniak, Meirav Zehavi   +5 more
core   +9 more sources

The Importance of Being Proper [PDF]

, 2014
In this paper we study two problems related to the drawing of level graphs, that is, T -Level Planarity and Clustered-Level Planarity. We show that both problems are NP -complete in the general case and that they become polynomial-time solvable when ...
Patrizio Angelini, Giordano Da Lozzo, Giuseppe Di Battista, Fabrizio Frati, Vincenzo Roselli   +4 more
openaire   +4 more sources

Overlapping cluster planarity [PDF]

2007 6th International Asia-Pacific Symposium on Visualization, 2007
Summary: This paper investigates a new direction in the area of cluster planarity by addressing the following question: Let G be a graph along with a hierarchy of vertex clusters, where clusters can partially intersect. Does G admit a drawing where each cluster is inside a simple closed region, no two edges intersect, and no edge intersects a region ...
DIDIMO, WALTER, GIORDANO, FRANCESCO, LIOTTA, Giuseppe   +2 more
openaire   +5 more sources