Article

# Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs

Department of Applied Mathematics and Physics, Kyoto University, Kioto, Kyoto, Japan
(Impact Factor: 0.79). 12/2005; 44(1):1-32. DOI: 10.1007/s00453-004-1144-8
Source: DBLP

ABSTRACT

Hierarchical graphs and clustered graphs are useful non-classical graph models for structured relational information. Hierarchical
graphs are
graphs with layering structures; clustered graphs are graphs with
recursive clustering structures. Both have applications in CASE tools, software visualization and VLSI design. Drawing algorithms
for hierarchical
graphs have been well investigated. However, the problem of planar straight-line representation has not been solved completely.
In this paper we answer the question: does every planar hierarchical graph admit a planar straight-line
hierarchical drawing? We present an algorithm that constructs
such drawings in linear time. Also, we answer a basic question for clustered
graphs, that is, does every planar clustered graph admit a planar
straight-line drawing with clusters drawn as convex polygons? We
provide a method for such drawings based on our algorithm for
hierarchical graphs.

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• "A particular attention has been devoted to straight-line convex drawings, that are c-planar drawings requiring edges to be straight-line segments and clusters to be convex regions. Every c-planar graph admits a straight-line convex drawing [10], even JGAA, 18(5) 633â€“675 (2014) 635 if the shape of each cluster is fixed in advance [1]. Straight-line convex drawings might require exponential area [14]. "
##### Article: Multilayer Drawings of Clustered Graphs
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ABSTRACT: The cluster adjacency graph of a flat clustered graph C(G, T) is the graph A whose vertices are the clusters in T and whose edges connect clusters containing vertices that are adjacent in G. A multilayer drawing of a clustered graph C consists of a straight-line c-planar drawing of C in which the clusters are drawn as convex regions and of a straight-line planar drawing of A such that each vertex a âˆˆ A is drawn in the cluster corresponding to a and such that no edge (a1, a2) âˆˆ A intersects any cluster different from a1 and a2. In this paper, we show that every c- planar flat clustered graph admits a multilayer drawing.
Preview · Article · Jan 2014 · Journal of Graph Algorithms and Applications
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• "The area of graph drawing has progressed considerably to the extent that there are now many layout algorithms for different drawing styles, from circular layout [6] [19], to hierarchical layout [14], orthogonal layout [15], and force-directed layout [13] [17] [24]. Efficiency and effectiveness of force-directed algorithms are further improved by the multilevel approach and fast force approximation [21] [22] [31], as well as by parallelization and the use of GPU [16] [3] [23]. "
##### Article: Intelligent Graph Layout Using Many Users' Input
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ABSTRACT: In this paper, we propose a new strategy for graph drawing utilizing layouts of many sub-graphs supplied by a large group of people in a crowd sourcing manner. We developed an algorithm based on Laplacian constrained distance embedding to merge subgraphs submitted by different users, while attempting to maintain the topological information of the individual input layouts. To facilitate collection of layouts from many people, a light-weight interactive system has been designed to enable convenient dynamic viewing, modification and traversing between layouts. Compared with other existing graph layout algorithms, our approach can achieve more aesthetic and meaningful layouts with high user preference.
Full-text · Article · Dec 2012 · IEEE Transactions on Visualization and Computer Graphics
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• "We present an algorithm to construct a convex drawing of clustered planar graphs. Note that this extends the previous known results on straight-line drawings of connected clustered planar graphs [7]. This paper is organized as follows: Section 2 reviews basic terminology. "
##### Article: Convex drawings of hierarchical planar graphs and clustered planar graphs
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ABSTRACT: Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in VLSI de- sign, CASE tools, software visualisation and visualisation of social networks and bi- ological networks. Straight-line drawing algorithms for hierarchical graphs and clus- tered graphs have been presented in (P. Eades, Q. Feng, X. Lin and H. Nagamochi, Straight-line drawing algorithms for hierarchical graphs and clustered graphs, Algo- rithmica, 44, pp. 1-32, 2006). A straight-line drawing is called a convex drawing if every facial cycle is drawn as a convex polygon. In this paper, it is proved that every internally triconnected hierarchical plane graph with the outer facial cycle drawn as a convex polygon admits a convex drawing. We present an algorithm which constructs such a drawing. We then extend our results to convex representations of clustered planar graphs. It is proved that every internally triconnected clustered plane graph with completely connected clustering structure admits a convex drawing. We present an algorithm to construct a convex drawing of clustered planar graphs.
Full-text · Article · Sep 2010 · Journal of Discrete Algorithms