Quasi-Upward Planar Drawings of Mixed Graphs with Few Bends: Heuristics and Exact Methods

Abstract

AbstractA mixed graph has both directed and undirected edges. We study how to compute a crossing-free drawing of a planar embedded mixed graph, such that it is upward “as much as possible”. Roughly speaking, in an upward drawing of a mixed graph all edges are monotone in the vertical direction and directed edges flow monotonically from bottom to top according to their orientation. We study quasi-upward drawings of mixed graphs, that is, upward drawings where edges can break the vertical monotonicity in a finite number of edge points, called bends. We describe both efficient heuristics and exact methods for computing quasi-upward planar drawings of planar embedded mixed graphs with few bends, and we extensively compare them experimentally: the results show the effectiveness of our algorithms in many cases.KeywordsInteger Linear ProgrammingDirected EdgeUndirected EdgeInteger Linear Programming ModelPlanar EmbeddingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.