Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2009-010 (April 06, 2009)

Visual Analysis of Hierarchical Data Using 2.5D Drawing with Minimum Occlusion
by Kazuya Haraguchi, Seok-Hee Hong, Hiroshi Nagamochi

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In this paper, we consider 2.5D drawing of a pair of trees which are connected by some edges, representing relationships between nodes, as an attempt to develop a tool for analyzing pairwise hierarchical data. We consider two ways of drawing such a graph, called parallel and perpendicular drawings, where the graph appears as a bipartite graph viewed from two orthogonal angles $X$ and $Y$. We define the occlusion of a drawing as the sum of the edge crossings that can be seen in the two angles, and propose algorithms to minimize the occlusion based on the fundamental one-sided crossing minimization problem. We also give some visualization examples of our method using phylogenetic trees and a mushroom database.