Untangling graphs representing spatial relationships driven by drawing aesthetics

Representing relational data, modeled as a graph, provides visual insight into several application areas. In practice, however, data may contain small but significant errors mainly due to human interaction. Here we address the problem of correcting misplaced edges of a given graph based on straight-line drawings in a plane. In such terms seeking for a solution on graphs that have no repeated pattern nor regular structure seems inapplicable. Therefore we focus on structured graphs representing spatial relationships, that arise in a wide range of applications, and we consider the quality of a drawing as a measure of a graph's correctness. To define an ordering among the modified graphs, we formalize the evaluation of a drawing with respect to certain aesthetic criteria. We give a polynomial-time algorithm that computes a modified graph with a better layout than the original graph when only single-edge replacements are allowed. We study the behavior of the algorithm and illustrate its results on several test sets taken from a sparse matrix collection. In all cases the proposed algorithm manages to identify and correct the misplaced edges within a small number of modifications.

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