Planar Drawings of Fixed-Mobile Bigraphs
Computational Geometry
2017-08-31 v1 Computational Complexity
Discrete Mathematics
Data Structures and Algorithms
Abstract
A fixed-mobile 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 poly-line drawing of G with at most k bends per edge. In the most general case, we show NP-hardness. For k=0 and under additional constraints on the positions of the fixed or mobile vertices, we either prove that the problem is polynomial-time solvable or prove that it belongs to NP. Finally, we present a polynomial-time testing algorithm for a certain type of "layered" 1-bend drawings.
Cite
@article{arxiv.1708.09238,
title = {Planar Drawings of Fixed-Mobile Bigraphs},
author = {Michael Bekos and Felice De Luca and Walter Didimo and Tamara Mchedlidze and Martin Nöllenburg and Antonios Symvonis and Ioannis Tollis},
journal= {arXiv preprint arXiv:1708.09238},
year = {2017}
}