Approximating minimum manhattan networks in higher dimensions

Aparna Das, Emden R. Gansner, Michael Kaufmann, Stephen G Kobourov, Joachim Spoerhase, Alexander Wolff

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

1 Citation (Scopus)

Abstract

We consider the minimum Manhattan network problem, which is defined as follows. Given a set of points called terminals in ℝd , find a minimum-length network such that each pair of terminals is connected by a set of axis-parallel line segments whose total length is equal to the pair's Manhattan (that is, L 1-) distance. The problem is NP-hard in 2D and there is no PTAS for 3D (unless P=NP ). Approximation algorithms are known for 2D, but not for 3D. We present, for any fixed dimension d and any ε O, an O(n ε-approximation. For 3D, we also give a 4(k-1)-approximation for the case that the terminals are contained in the union of κ≥2 parallel planes.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages49-60
Number of pages12
Volume6942 LNCS
DOIs
StatePublished - 2011
Event19th Annual European Symposium on Algorithms, ESA 2011 - Saarbrucken, Germany
Duration: Sep 5 2011Sep 9 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6942 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other19th Annual European Symposium on Algorithms, ESA 2011
CountryGermany
CitySaarbrucken
Period9/5/119/9/11

Fingerprint

Approximation algorithms
Higher Dimensions
Computational complexity
Approximation
Line segment
Set of points
Approximation Algorithms
Union
NP-complete problem

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Das, A., Gansner, E. R., Kaufmann, M., Kobourov, S. G., Spoerhase, J., & Wolff, A. (2011). Approximating minimum manhattan networks in higher dimensions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6942 LNCS, pp. 49-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6942 LNCS). https://doi.org/10.1007/978-3-642-23719-5_5

Approximating minimum manhattan networks in higher dimensions. / Das, Aparna; Gansner, Emden R.; Kaufmann, Michael; Kobourov, Stephen G; Spoerhase, Joachim; Wolff, Alexander.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6942 LNCS 2011. p. 49-60 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6942 LNCS).

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

Das, A, Gansner, ER, Kaufmann, M, Kobourov, SG, Spoerhase, J & Wolff, A 2011, Approximating minimum manhattan networks in higher dimensions. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 6942 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6942 LNCS, pp. 49-60, 19th Annual European Symposium on Algorithms, ESA 2011, Saarbrucken, Germany, 9/5/11. https://doi.org/10.1007/978-3-642-23719-5_5
Das A, Gansner ER, Kaufmann M, Kobourov SG, Spoerhase J, Wolff A. Approximating minimum manhattan networks in higher dimensions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6942 LNCS. 2011. p. 49-60. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-23719-5_5
Das, Aparna ; Gansner, Emden R. ; Kaufmann, Michael ; Kobourov, Stephen G ; Spoerhase, Joachim ; Wolff, Alexander. / Approximating minimum manhattan networks in higher dimensions. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6942 LNCS 2011. pp. 49-60 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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