International Symposium on Graph Drawing and Network Visualization

Graph Drawing and Network Visualization pp 395-408

# On Embeddability of Buses in Point Sets

• Till Bruckdorfer
• Michael Kaufmann
• Stephen G. Kobourov
• Sergey Pupyrev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9411)

## Abstract

Set membership of points in the plane can be visualized by connecting corresponding points via graphical features, like paths, trees, polygons, ellipses. In this paper we study the bus embeddability problem (BEP): given a set of colored points we ask whether there exists a planar realization with one horizontal straight-line segment per color, called bus, such that all points with the same color are connected with vertical line segments to their bus. We present an ILP and an FPT algorithm for the general problem. For restricted versions of this problem, such as when the relative order of buses is predefined, or when a bus must be placed above all its points, we provide efficient algorithms. We show that another restricted version of the problem can be solved using 2-stack pushall sorting. On the negative side we prove the NP-completeness of a special case of BEP.

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© Springer International Publishing Switzerland 2015

## Authors and Affiliations

• Till Bruckdorfer
• 1
• Michael Kaufmann
• 1
• Stephen G. Kobourov
• 2
• Sergey Pupyrev
• 2
• 3
1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany
2. 2.Department for Computer ScienceUniversity of ArizonaTucsonUSA
3. 3.Institute of Mathematics and Computer ScienceUral Federal UniversityYekaterinburgRussia