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In this paper, we present a method to plot a directed acyclic graph (DAG) which represents a hierarchical structure with multiple inheritances. This method is used in the thesaurus browser `xthes' to ...display 'is-a' relationship between nodes in a thesaurus or ontology. Because it is noted that the problem of minimizing arc crossings in a DAG is NP-hard, we need a fast heuristic algorithm. `xthes' draws a DAG as follows. At first, it splits a DAG into a tree and other non-tree arcs. Then, it rearranges the order of children nodes by clustering subtrees, and reverses the order of subtrees in the clusters, to make the length of inter-subtree links as short as possible. Finally, it minimizes the distance between subtrees in bottom-up manner, and decides the position of the nodes and arcs. By the experiment, it was confirmed that our node-exchanging method saves about 50% of the total length of the crossing arcs. It seems that our method can display a DAG in a comprehensible form, and that it is fast enough to update the diagram interactively.show more
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