## ImPrEd: An Improved Force-Directed Algorithm that Prevents Nodes from Crossing Edges (2011)

Citations: | 1 - 0 self |

### BibTeX

@MISC{Simonetto11impred:an,

author = {Paolo Simonetto and Daniel Archambault and David Auber and Romain Bourqui and Université Bordeaux Inria and Bordeaux Sud-ouest},

title = {ImPrEd: An Improved Force-Directed Algorithm that Prevents Nodes from Crossing Edges},

year = {2011}

}

### OpenURL

### Abstract

PrEd [Ber00] is a force-directed algorithm that improves the existing layout of a graph while preserving its edge crossing properties. The algorithm has a number of applications including: improving the layouts of planar graph drawing algorithms, interacting with a graph layout, and drawing Euler-like diagrams. The algorithm ensures that nodes do not cross edges during its execution. However, PrEd can be computationally expensive and overlyrestrictive in terms of node movement. In this paper, we introduce ImPrEd: an improved version of PrEd that overcomes some of its limitations and widens its range of applicability. ImPrEd also adds features such as flexible or crossable edges, allowing for greater control over the output. Flexible edges, in particular, can improve the distribution of graph elements and the angular resolution of the input graph. They can also be used to generate Euler diagrams with smooth boundaries. As flexible edges increase data set size, we experience an execution/drawing quality trade off. However, when flexible edges are not used, ImPrEd proves to be consistently faster than PrEd. Categories and Subject Descriptors (according to ACM CCS): G.2.2 [Discrete Mathematics]: Graph Theory—Graph Algorithms

### Citations

1033 |
Computational Geometry: Algorithms and Applications
- Berg, Kreveld, et al.
- 2000
(Show Context)
Citation Context ...odes must remain on the same side of all defining half planes of the region. Therefore, Rv contains any future position of any node v and Re, being convex, as it is the intersection of convex regions =-=[DBCVKO00]-=-, fully contains any final position of the edge e. Since Rv ⊆ Rv(v,e), Re ⊆ Re(v,e), and Rv(v,e) ∩ Re(v,e) = ∅ for every node v and every non-incident edge e, no node can cross an edge when moving. Th... |

468 | Graph drawing by force-directed placement - Fruchterman, Reingold - 1991 |

369 | Graph visualization and navigation in information visualization: a survey
- Herman, Melancon, et al.
- 2000
(Show Context)
Citation Context ...ever, this algorithm does not preserve all crossings in the initial layout. 2.4. Planar Graph Drawing and Visualisation Graph visualisation systems are often less interested in strict graph planarity =-=[HMM00]-=-, since a large graph rarely admits a strict, planar embedding. However, planar graphs are often created to provide an overview of the data. Also, they have recently become of interest to the problem ... |

347 |
Graph Drawing: Algorithms for the Visualization of Graphs
- Battista, Eades, et al.
- 1999
(Show Context)
Citation Context ... ( ¯F) and B e ( ¯F) of the faces in ¯F (see Figure 2d). Let us assume that G is not a plane graph. To apply the above-described method, G is reduced to a plane graph, ˆG, through planar augmentation =-=[DBETT98]-=-. We label all nodes and edges of ˆG using elements that generated them, and these labels are used to compute Sv. The nodes of ˆG that do not correspond to a node in G are not labeled and are not cons... |

156 |
How to draw a planar graph on a grid
- Fraysseix, Pach, et al.
- 1990
(Show Context)
Citation Context ...f nodes and restricts their movement to guarantee this property. The author of PrEd suggested two possible applications: improving the layout [Pur97] of planar, straight-line graph drawing algorithms =-=[DFPP90]-=- and driving force-directed graph layout interactively. By realising that not only does PrEd preserve all edge crossings in an existing layout but actually prevents nodes from crossing edges, we can a... |

137 |
Which aesthetic has the greatest effect on human understanding
- Purchase
- 1997
(Show Context)
Citation Context ... layout. The algorithm computes the maximal displacement of nodes and restricts their movement to guarantee this property. The author of PrEd suggested two possible applications: improving the layout =-=[Pur97]-=- of planar, straight-line graph drawing algorithms [DFPP90] and driving force-directed graph layout interactively. By realising that not only does PrEd preserve all edge crossings in an existing layou... |

101 | A heuristic for graph drawing. Congressus Numerantium - Eades - 1984 |

45 |
FADE: Graph drawing, clustering, and visual abstraction
- Quigley, Eades
- 2001
(Show Context)
Citation Context ...3). 4.2. QuadTrees We use QuadTrees to determine with sublinear complexity the nodes N d v and edges E d v at a distance d from a node v. The data structure has been used in force-directed algorithms =-=[QE01]-=- as distant elements can often be approximated or ignored. In ImPrEd, when computing F r and F e , we only consider nodes in N 3δ v and the edges E γ v. The set of nearby edges can also be used to red... |

43 | Graphael: Graph animations with evolving layouts - Erten, Harding, et al. - 2003 |

36 | Online dynamic graph drawing - Frishman, Tal - 2008 |

30 | IPSep-CoLa: An incremental procedure for separation constraint layout of graphs - Dwyer, Koren, et al. - 2006 |

26 |
A force-directed algorithm that preserves edge-crossing properties
- Bertault
(Show Context)
Citation Context ...Daniel Archambault 2 , David Auber 1 , and Romain Bourqui 1 1 LaBRI, Université Bordeaux 1 — INRIA, Bordeaux Sud-Ouest 2 University College Dublin inria-00605921, version 1 - 8 Aug 2011 Abstract PrEd =-=[Ber00]-=- is a force-directed algorithm that improves the existing layout of a graph while preserving its edge crossing properties. The algorithm has a number of applications including: improving the layouts o... |

24 |
Heiko Mehldau. A Fast Adaptive Layout Algorithm for Undirected Graphs
- Frick, Ludwig
- 1994
(Show Context)
Citation Context ...ciently. In fact, the force system of PrEd might push disconnected components apart indefinitely as there is only a repulsive force between these elements. Inspired by other force-directed algorithms =-=[FLM95]-=-, ImPrEd has a gravity force F g that attracts nodes to the barycentre of the graph with constant magnitude. This force prevents the previously described behaviour and helps maintain a good aspect rat... |

23 | Planar polyline drawings with good angular resolution - Gutwenger, Mutzel - 1998 |

20 | TAL A.: Dynamic Drawing of Clustered Graphs - FRISHMAN |

16 | GMap: Visualizing graphs and clusters as maps
- Gansner, Hu
- 2010
(Show Context)
Citation Context ...ler-like diagram generation. As future work, we would like to investigate new application fields for ImPrEd. For instance, the algorithm could be applied to combined graph-map drawings, such as GMaps =-=[GHK10]-=-. The running time improvement could also be further studied in terms of its performance with respect to edge density. However, ImPrEd still has problems scaling to large graphs. To overcome this limi... |

13 | Dig-CoLa: Directed Graph Layout through Constrained Energy Minimization - Dwyer, Koren - 2005 |

11 |
Planar Graph Drawing
- Rahman
- 2004
(Show Context)
Citation Context ... is restricted. 3. Definitions Before describing the algorithm, we review a few definitions and introduce some notation. A more detailed explanation can be found in graph theory and drawing textbooks =-=[NR04]-=-. Let G = (V,E) be a simple undirected graph. An embedding, or planar drawing, of G is a representation of the graph submitted to Eurographics / IEEE Symposium on Visualization 2011 (EuroVis 2011)P. ... |

8 | C.: Visualizing internet evolution on the autonomous systems level
- Boitmanis, Brandes, et al.
- 2008
(Show Context)
Citation Context ...s have impeded the movement of nodes via geometric restriction [SP08]. For energy-based approaches, penalising terms can be added to discourage nodes from moving too far from their previous positions =-=[BBP08]-=-. These approaches modify their respective algorithms to drive nodes in the layout towards certain positions. However, they do not guarantee that a node will stay in a particular region of the plane o... |

8 | M.: Topology preserving constrained graph layout - Dwyer, Marriott, et al. |

8 | A Hybrid Space-Filling and Force-Directed Layout Method for Visualizing Multiple-Category Graphs
- Itoh, Muelder, et al.
- 2009
(Show Context)
Citation Context ...to et al. [SAA09]. Sets are films extracted from the IMDb top-chart and contain the full credited actor list. The second diagram (10 sets, 176 elements) is a small protein-protein interaction network =-=[IMMS09]-=- where nodes are placed into multiple sets with network edges included. The first diagram’s graphs are iGraphA and gGraphA, and the second diagram’s graphs are iGraphB and gGraphB. submitted to Eurogr... |

4 |
Topology-driven force-directed algorithms
- Didimo, Liotta, et al.
- 2011
(Show Context)
Citation Context ... However, with ImPrEd, we aim at the specific application of node containment which may be handled more simply with a targeted algorithm. 2.3. Topology-Driven, Force-Directed Algorithms Didimo et al. =-=[DLR11]-=- proposed a framework, combining force-directed and planarisation-based approaches for graph drawing. This hybrid algorithm aims at drawing graphs with a small number of crossings and high angular res... |

4 | versatile and simple constrained graph layout - Scalable |