Layered Graph Drawing with Few Gaps and Few Crossings

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.