Planar Drawings of FixedMobile BigraphsBekos, Michael A. and De Luca, Felice and Didimo, Walter and Mchedlidze, Tamara and Nöllenburg, Martin and Symvonis, Antonios and Tollis, Ioannis G. (2017) Planar Drawings of FixedMobile Bigraphs. In: Graph Drawing and Network Visualization. GD 2017, September 2527 , pp. 426439(Official URL: https://doi.org/10.1007/9783319739151_33). Full text not available from this repository.
Official URL: https://doi.org/10.1007/9783319739151_33
AbstractA fixedmobile bigraph G is a bipartite graph such that the vertices of one partition set are given with fixed positions in the plane and the mobile vertices of the other part, together with the edges, must be added to the drawing. We assume that G is planar and study the problem of finding, for a given k≥0, a planar polyline drawing of G with at most k bends per edge. In the most general case, we show NPhardness. For k=0 and under additional constraints on the positions of the fixed or mobile vertices, we either prove that the problem is polynomialtime solvable or prove that it belongs to NP. Finally, we present a polynomialtime testing algorithm for a certain type of “layered” 1bend drawings. Research in this work started at the Bertinoro Workshop on Graph Drawing 2016. We thank all the participants and in particular S.H. Hong for useful discussions. We also thank an anonymous reviewer of this research for some valuable comments, and especially for suggesting the idea behind the proof of Theorem 6.
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