Approximating minimum manhattan networks in higher dimensions

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

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

1 Scopus citations

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 publicationAlgorithms, ESA 2011 - 19th Annual European Symposium, Proceedings
Pages49-60
Number of pages12
DOIs
StatePublished - Sep 20 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)0302-9743
ISSN (Electronic)1611-3349

Other

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Das, A., Gansner, E. R., Kaufmann, M., Kobourov, S., Spoerhase, J., & Wolff, A. (2011). Approximating minimum manhattan networks in higher dimensions. In Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings (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