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Efficient visual navigation of hierarchically structured graphs

Effiziente visuelle Navigation in hierarchisch strukturierten Graphen

  • Visual navigation of hierarchically structured graphs is a technique for interactively exploring large graphs that possess an additional hierarchical structure. This structure is expressed in form of a recursive clustering of the nodes: in call graphs of telephone networks, for instance, the nodes are identified with phone numbers; they are clustered recursively through the implicit structure of the numbers, e. g., nodes with the same area code belong to a cluster. In order to reduce the complexity and the size of the graph, only those subgraphs that are currently needed are shown in detail, while the others are collapsed, i. e., represented by meta nodes. In such a graph view the subgraphs in the areas of interest are expanded furthest, whereas those on the periphery are abstracted. As the areas of interest change over time, clusters in a view need to be expanded or contracted. First and foremost, there is need for an efficient data structure for this graph view maintenance problem. Depending on the admissible modifications of theVisual navigation of hierarchically structured graphs is a technique for interactively exploring large graphs that possess an additional hierarchical structure. This structure is expressed in form of a recursive clustering of the nodes: in call graphs of telephone networks, for instance, the nodes are identified with phone numbers; they are clustered recursively through the implicit structure of the numbers, e. g., nodes with the same area code belong to a cluster. In order to reduce the complexity and the size of the graph, only those subgraphs that are currently needed are shown in detail, while the others are collapsed, i. e., represented by meta nodes. In such a graph view the subgraphs in the areas of interest are expanded furthest, whereas those on the periphery are abstracted. As the areas of interest change over time, clusters in a view need to be expanded or contracted. First and foremost, there is need for an efficient data structure for this graph view maintenance problem. Depending on the admissible modifications of the graph and its hierarchical clustering, three variants have been discussed in the literature: in the static case, everything is fixed; in the dynamic graph variant, only edges of the graph can be inserted and deleted; finally, in the dynamic graph and tree variant the graph additionally is subject to node insertions and deletions and the clustering may change through splitting and merging of clusters. We introduce a new variant, dynamic leaves, which is based on the dynamic graph variant, but additionally allows insertion and deletion of graph nodes, i. e., leaves of the hierarchy. So far efficient data structures were known only for the static and the dynamic graph variant, i. e., neither the nodes of the graph nor the clustering could be modified. As this is unsatisfactory in an interactive editor for hierarchically structured graphs, we first generalize the approach of Buchsbaum et. al (Proc. 8th ESA, vol. 1879 of LNCS, pp. 120–131, 2000), in which graph view maintenance is formulated as a special case of range searching over tree cross products, to the new dynamic leaves variant. This generalization builds on a novel technique of superimposing a search tree over an ordered list maintenance structure. With an additional factor of roughly O(log n/log log n), this is the first data structure for the problem of graph view maintenance where the node set is dynamic. Visualizing the expanding and contracting appropriately is the second challenge. We propose a local update scheme for the algorithm of Sugiyama and Misue (IEEE Trans. on Systems, Man, and Cybernetics 21 (1991) 876– 892) for drawing compound digraphs. The layered drawings that it produces have many applications ranging from biochemical pathways to UML diagrams. Modifying the intermediate results of every step of the original algorithm locally, the update scheme is more efficient than re-applying the entire algorithm after expansion or contraction. As our experimental results on randomly generated graphs show, the average time for updating the drawing is around 50 % of the time for redrawing for dense graphs and below 20 % for sparse graphs. Also, the performance gain is not at the expense of quality as regards the area of the drawing, which increases only insignificantly, and the number of crossings, which is reduced. At the same time, the locality of the updates preserves the user ’s mental map of the graph: nodes that are are not affected stay on the same level in the same relative order and expanded edges take the same course as the corresponding contracted edge; furthermore, expansion and contraction are visually inverse. Finally, our new data structure and the update scheme are combined into an interactive editor and viewer for compound (di-)graphs. A flexible and extensible software architecture is introduced that lays the ground for future research. It employs the well-known Model-View-Controller (MVC) paradigm to separate the abstract data from its presentation. As a consequence, the purely combinatorial parts, i. e., the compound (di-)graph and its views, are reusable without the editor front-end. A proof-of-concept implementation based on the proposed architecture shows its feasibility and suitability.show moreshow less

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Metadaten
Author:Marcus Raitner
URN:urn:nbn:de:bvb:739-opus-658
Advisor:Franz J. Brandenburg
Document Type:Doctoral Thesis
Language:English
Year of Completion:2005
Date of Publication (online):2006/02/21
Publishing Institution:Universität Passau
Granting Institution:Universität Passau, Fakultät für Informatik und Mathematik
Date of final exam:2006/02/08
Release Date:2006/02/21
GND Keyword:Dynamische Datenstruktur; Kognitive Landkarte; Graphenzeichnen
Institutes:Fakultät für Informatik und Mathematik / Mitarbeiter Lehrstuhl/Einrichtung der Fakultät für Informatik und Mathematik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
open_access (DINI-Set):open_access
Licence (German):License LogoStandardbedingung laut Einverständniserklärung