IEEE Transactions on Visualization and Computer Graphics
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Edges and switches, tunnels and bridges
Computational Geometry: Theory and Applications
Algorithms for variable-weighted 2-SAT and dual problems
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Multilevel agglomerative edge bundling for visualizing large graphs
PACIFICVIS '11 Proceedings of the 2011 IEEE Pacific Visualization Symposium
Using the Gestalt Principle of Closure to Alleviate the Edge Crossing Problem in Graph Drawings
IV '11 Proceedings of the 2011 15th International Conference on Information Visualisation
Evaluating partially drawn links for directed graph edges
GD'11 Proceedings of the 19th international conference on Graph Drawing
SideKnot: Revealing relation patterns for graph visualization
PACIFICVIS '12 Proceedings of the 2012 IEEE Pacific Visualization Symposium
Mad at edge crossings? break the edges!
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
Force-directed edge bundling for graph visualization
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
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Recently, a new way of avoiding crossings in straight-line drawings of non-planar graphs has been investigated. The idea of partial edge drawings (PED) is to drop the middle part of edges and rely on the remaining edge parts called stubs. We focus on a symmetric model (SPED) that requires the two stubs of an edge to be of equal length. In this way, the stub at the other endpoint of an edge assures the viewer of the edge's existence. We also consider an additional homogeneity constraint that forces the stub lengths to be a given fraction δ of the edge lengths (δ-SHPED). Given length and direction of a stub, this model helps to infer the position of the opposite stub. We show that, for a fixed stub---edge length ratio δ, not all graphs have a δ-SHPED. Specifically, we show that K241 does not have a 1/4-SHPED, while bandwidth-k graphs always have a $\Theta(1/\sqrt{k})$-SHPED. We also give bounds for complete bipartite graphs. Further, we consider the problem MaxSPED where the task is to compute the SPED of maximum total stub length that a given straight-line drawing contains. We present an efficient solution for 2-planar drawings and a 2-approximation algorithm for the dual problem.