On embeddability of buses in point sets

Till Bruckdorfer, Michael Kaufmann, Stephen G Kobourov, Sergey Pupyrev

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages395-408
Number of pages14
Volume9411
ISBN (Print)9783319272603
DOIs
StatePublished - 2015
Event23rd International Symposium on Graph Drawing and Network Visualization, GD 2015 - Los Angeles, United States
Duration: Sep 24 2015Sep 26 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9411
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other23rd International Symposium on Graph Drawing and Network Visualization, GD 2015
CountryUnited States
CityLos Angeles
Period9/24/159/26/15

Fingerprint

Embeddability
Point Sets
Line segment
NP-completeness
Color
Inductive logic programming (ILP)
Sorting
Straight Line
Polygon
Horizontal
Efficient Algorithms
Vertical
Path

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Bruckdorfer, T., Kaufmann, M., Kobourov, S. G., & Pupyrev, S. (2015). On embeddability of buses in point sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9411, pp. 395-408). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9411). Springer Verlag. https://doi.org/10.1007/978-3-319-27261-0_33

On embeddability of buses in point sets. / Bruckdorfer, Till; Kaufmann, Michael; Kobourov, Stephen G; Pupyrev, Sergey.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9411 Springer Verlag, 2015. p. 395-408 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9411).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bruckdorfer, T, Kaufmann, M, Kobourov, SG & Pupyrev, S 2015, On embeddability of buses in point sets. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 9411, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9411, Springer Verlag, pp. 395-408, 23rd International Symposium on Graph Drawing and Network Visualization, GD 2015, Los Angeles, United States, 9/24/15. https://doi.org/10.1007/978-3-319-27261-0_33
Bruckdorfer T, Kaufmann M, Kobourov SG, Pupyrev S. On embeddability of buses in point sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9411. Springer Verlag. 2015. p. 395-408. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-27261-0_33
Bruckdorfer, Till ; Kaufmann, Michael ; Kobourov, Stephen G ; Pupyrev, Sergey. / On embeddability of buses in point sets. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 9411 Springer Verlag, 2015. pp. 395-408 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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