Layered Graph Drawing with Few Gaps and Few Crossings
Alexander Dobler, Jakob Roithinger
TL;DR
The paper tackles readability-enhancing constraints in layered graph drawings by restricting the placement of dummy nodes, introducing OSCM-SG and OSCM-$k$G as gap-bounded variants of the classic one-sided crossing minimization problem. It develops transformation-based approximation methods that preserve ratios from OSCM to OSCM-SG, and introduces a dynamic-programming approach to handle multiple gaps in OSCM-$k$G, with proven runtime bounds. An exact ILP formulation for OSCM-$k$G complements the heuristics, enabling direct comparisons to evaluate solution quality. Experimental results on synthetic graphs demonstrate that the proposed gap-restricted methods achieve competitive crossing counts while offering tractable runtimes, highlighting practical benefits for scalable, readable layered drawings.
Abstract
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings between edges, increasing readability. Usually, this is done by repeated one-sided crossing minimization for each layer. These algorithms allow edges that connect nodes on non-neighboring layers, called ``long'' edges, to weave freely throughout layers of the graph, creating many ``gaps'' in each layer. As shown in a recent work on hive plots -- a similar visualization drawing vertices on multiple layers -- it can be beneficial to restrict the number of such gaps. We extend existing heuristics and exact algorithms for one-sided crossing minimization in a way that restricts the number of allowed gaps. The extended heuristics maintain approximation ratios, and in an experimental evaluation we show that they perform well with respect to the number of resulting crossings when compared with exact ILP formulations.