Depth-first layout algorithm for trees

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Abstract

This paper deals with a layout problem of trees satisfying certain given aesthetic conditions. It is known as “tidy drawing problems of trees”. We consider a type of tree called a “tree-structured diagram” in which each node has variable size and location.

In this paper, for drawing tree-type program flowcharts, we first formulate “tidy drawing problems of tree-structured diagrams” on the integral lattice. The formulation defines a tree-structured diagram and aesthetic conditions, which are modifications of the tidy drawing problem of trees. Second, we develop O(n)- and O(n2)-time algorithms to provide layouts which satisfy the conditions introduced. As a result, we obtain the relationship between the aesthetic conditions and the time complexity of algorithms.

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