Fully Dynamic 3-Dimensional Orthogonal Graph Drawing

Abstract

In a 3-dimensional orthogonal drawing of a graph, vertices are mapped to grid points on an integer lattice and edges are routed along integer grid lines. In this paper, we present a layout scheme that draws any graph with n vertices of maximum degree 6, using at most 6 bends per edge and in a volume of O(n ²). The advantage of our strategy over other drawing methods is that our method is fully dynamic, allowing both insertion and deletion of vertices and edges, while maintaining the volume and bend bounds. The drawing can be obtained in O(n) time and insertions/deletions can be performed in O(1) time. Multiple edges and self loops are permitted. A more elaborate construction that uses only 5 bends per edge, and a simpler, more balanced layout that requires at most 7 bends per edge are also described.

N.S.E.R.C. is gratefully thanked for financial assistance.

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