Constrained Graph Layout Research Articles

A generic algorithm for layout of biological networks

BackgroundBiological networks are widely used to represent processes in biological systems and to capture interactions and dependencies between biological entities. Their size and complexity is steadily increasing due to the ongoing growth of knowledge in the life sciences. To aid understanding of biological networks several algorithms for laying out and graphically representing networks and network analysis results have been developed. However, current algorithms are specialized to particular layout styles and therefore different algorithms are required for each kind of network and/or style of layout. This increases implementation effort and means that new algorithms must be developed for new layout styles. Furthermore, additional effort is necessary to compose different layout conventions in the same diagram. Also the user cannot usually customize the placement of nodes to tailor the layout to their particular need or task and there is little support for interactive network exploration.ResultsWe present a novel algorithm to visualize different biological networks and network analysis results in meaningful ways depending on network types and analysis outcome. Our method is based on constrained graph layout and we demonstrate how it can handle the drawing conventions used in biological networks.ConclusionThe presented algorithm offers the ability to produce many of the fundamental popular drawing styles while allowing the exibility of constraints to further tailor these layouts.

Scalable, Versatile and Simple Constrained Graph Layout

AbstractWe describe a new technique for graph layout subject to constraints. Compared to previous techniques the proposed method is much faster and scalable to much larger graphs. For a graph with n nodes, m edges and c constraints it computes incremental layout in time O(n log n+m+c) per iteration. Also, it supports a much more powerful class of constraint: inequalities or equalities over the Euclidean distance between nodes. We demonstrate the power of this technique by application to a number of diagramming conventions which previous constrained graph layout methods could not support. Further, the constraint‐satisfaction method—inspired by recent work in position‐based dynamics—is far simpler to implement than previous methods.

Exploration of Networks using overview+detail with Constraint-based cooperative layout

A standard approach to large network visualization is to provide an overview of the network and a detailed view of a small component of the graph centred around a focal node. The user explores the network by changing the focal node in the detailed view or by changing the level of detail of a node or cluster. For scalability, fast force-based layout algorithms are used for the overview and the detailed view. However, using the same layout algorithm in both views is problematic since layout for the detailed view has different requirements to that in the overview. Here we present a model in which constrained graph layout algorithms are used for layout in the detailed view. This means the detailed view has high-quality layout including sophisticated edge routing and is customisable by the user who can add placement constraints on the layout. Scalability is still ensured since the slower layout techniques are only applied to the small subgraph shown in the detailed view. The main technical innovations are techniques to ensure that the overview and detailed view remain synchronized, and modifying constrained graph layout algorithms to support smooth, stable layout. The key innovation supporting stability are new dynamic graph layout algorithms that preserve the topology or structure of the network when the user changes the focus node or the level of detail by in situ semantic zooming. We have built a prototype tool and demonstrate its use in two application domains, UML class diagrams and biological networks.

Constrained graph layout by stress majorization and gradient projection

The adoption of the stress-majorization method from multi-dimensional scaling into graph layout has provided an improved mathematical basis and better convergence properties for so-called “force-directed placement” techniques. In this paper we explore algorithms for augmenting such stress-majorization techniques with simple linear constraints using gradient-projection optimization techniques. Our main focus is a particularly simple class of constraints called “orthogonal-ordering constraints” but we also discuss how gradient-projection methods may be extended to solve more general linear “separation constraints”. In addition, we demonstrate several graph-drawing applications where these types of constraints can be very useful.

Constrained Graph Layout

Most current graph layout technology does not lend itself to interactive applications such as animation or advanced user interfaces. We introduce the constrained graph layout model which is better suited for interactive applications. In this model, input to the layout module includes suggested positions for nodes and constraints over the node positions in the graph to be laid out. We describe four implementations of layout modules which are based on the constrained graph layout model. The first three implementations are for undirected graph layout while the fourth is for tree layout. The implementations use active set techniques to solve the layout. Our empirical evaluation shows that they are quite fast and give reasonable layout.