FORBID: Fast Overlap Removal by Stochastic GradIent Descent for Graph Drawing

Guaranteed Visibility in Scatterplots with Tolerance

“…VPSC [7,8] and Diamond [26] are two constraint-based algorithms that explicitly model the overlaps (or non-overlaps) as a set of constraints to relax and optimize. Finally, PRISM [9], GTree [30] and FORBID [10] model the distances to preserve (i.e., between non-overlapped nodes) and those to satisfy (i.e., between overlapped nodes) as a stress function to optimize. Stress is usually denoted σ and defined as:…”

“…FORBID [10] is the closest method to GIST as it was used as a backbone to build our algorithm. The algorithm's originality is to interlace two main components: a binary search for an optimal scale ratio, and Nodes Dispersion modeled as stress and optimized by Stochastic Gradient Descent [40].…”

“…PRISM and GTree implementations are taken from the Microsoft Automatic Graph Layout (MSAGL) library [31] and were executed on an Intel Core i7-9700K. We do not include FORBID [10] algorithm in this evaluation as it did not complete on scatterplots with N > 50000 (out of memory), and produced overlap-free layouts with too much nodes dispersion when it did complete.…”

“…Time costs. Since GIST backbone leverages FORBID [10], its complexity inherits from FORBID's one in O(s(N 2 + N log(N)) where s is the depth of the binary search. The N 2 complexity comes from the optimization of distance between all pairs of nodes.…”

“…GS methods [7-10, 14, 16, 29, 30, 33] produce exact solutions to the overlap removal problem. While some of these methods strongly rely on the scan line algorithm to process the data points sequentially (e.g., [14,16,29,33]), others model the overlap removal problem as a stress optimization (e.g., [9,10,30]). However, none of them have sub-quadratic complexity and they hardly scale well to large datasets.…”