Algorithms for Drawing Media

Eppstein, David

doi:10.1007/978-3-540-31843-9_19

Cited by 15 publications

(28 citation statements)

References 15 publications

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“…Most of the ideas in the following result are from Bose et al [4], but we elaborate on that paper to show that linear time recognition of arrangement graphs is possible. (See [9] for a more complicated linear time algorithm that recognizes the dual graphs of a wider class of arrangement graphs, the graphs of weak pseudoline arrangements in which pairs of pseudolines need not cross) Lemma 1. If we are given as input a graph G, then in linear time we can determine whether it is a pseudoline arrangement graph, determine its (unique) embedding as an arrangement graph, and find a pseudoline arrangement for which it is the arrangement graph.…”

Section: Preliminariesmentioning

confidence: 99%

Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity

Eppstein¹

2014

JGAA

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We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any \epsilon>0; finding such an input would represent significant progress on the famous k-set problem from discrete geometry. Drawing line arrangement graphs is the main task in the Planarity puzzle.Comment: 12 pages, 8 figures. To appear at 21st Int. Symp. Graph Drawing, Bordeaux, 201

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Section: Preliminariesmentioning

confidence: 99%

Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity

Eppstein¹

2014

JGAA

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“…(See [12] for a more complicated linear time algorithm that recognizes the dual graphs of a wider class of arrangement graphs, the graphs of weak pseudoline arrangements in which pairs of pseudolines need not cross) Lemma 1. If we are given as input a graph G, then in linear time we can determine whether it is a pseudoline arrangement graph, determine its (unique) embedding as an arrangement graph, and find a pseudoline arrangement for which it is the arrangement graph.…”

Section: Preliminariesmentioning

confidence: 99%

Drawing Arrangement Graphs in Small Grids, or How to Play Planarity

Eppstein

2013

Graph Drawing

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Abstract. We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n 7/6 ). No known input causes our algorithm to use area Ω(n 1+ ) for any > 0; finding such an input would represent significant progress on the famous k-set problem from discrete geometry. Drawing line arrangement graphs is the main task in the Planarity puzzle.

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“…Important subclasses of the partial cubes include trees [15] and median graphs [14]; Chepoi et al [3] discuss several other classes characterized in terms of their planar embeddings, including the benzenoid graphs arising from organic chemistry [17]. Partial cubes admit more efficient algorithms than arbitrary graphs for several important problems including unweighted all-pairs shortest paths [8] and are the basis for several specialized graph drawing algorithms [6].…”

Section: Introductionmentioning

confidence: 99%