Sloggy drawings of graphs

Abstract

We extend the recently introduced slanted-orthogonal (for short: slog) drawing model to a new relaxed model that we call sloggy, which allows crossings not exclusively on diagonals but also on rectilinear edge segments. Because of that, sloggy drawings might require much less bends than the corresponding drawings in the slog drawing model. On the positive side, we prove a closed-form formula on the number of bends of sloggy drawings. In contrast to this positive result, we show that there exist graphs whose sloggy drawings require exponential area. Since the complexity of the problem is still unknown and there is no polynomial-time algorithm to compute sloggy drawings, we give an ILP formulation that results in sloggy drawings that are optimal with respect to an objective function that weights the total number of diagonal crossings against the number of bends per edge.