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

Binucci, Carla; Didimo, Walter

doi:10.1007/978-3-319-04657-0_28

Cited by 3 publications

(2 citation statements)

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“…They also describe a branch-and-bound algorithm in the variable embedding setting. A list of papers about quasi-upward planarity also includes [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

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Quasi-upward Planar Drawings with Minimum Curve Complexity

Binucci¹,

Giacomo²,

Liotta³

et al. 2021

Preprint

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This paper studies the problem of computing quasi-upward planar drawings of bimodal plane digraphs with minimum curve complexity, i.e., drawings such that the maximum number of bends per edge is minimized. We prove that every bimodal plane digraph admits a quasiupward planar drawing with curve complexity two, which is worst-case optimal. We also show that the problem of minimizing the curve complexity in a quasi-upward planar drawing can be modeled as a min-cost flow problem on a unit-capacity planar flow network. This gives rise to an Õ(m 4 3 )-time algorithm that computes a quasi-upward planar drawing with minimum curve complexity; in addition, the drawing has the minimum number of bends when no edge can be bent more than twice. For a contrast, we show bimodal planar digraphs whose bend-minimum quasi-upward planar drawings require linear curve complexity even in the variable embedding setting.

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“…They also describe a branch-and-bound algorithm in the variable embedding setting. A list of papers about quasi-upward planarity also includes [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

“…The curve complexity is the maximum number of bends along any edge of the drawing. We recall that minimizing the curve complexity is a classical subject of investigation in Graph Drawing (see, e.g., [2,5,7,11,14,15,16,24,26,27]). Our results can be summarized as follows.…”

Section: Introductionmentioning

confidence: 99%