Approximating minimum manhattan networks in higher dimensions

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

doi:10.1007/978-3-642-23719-5_5

Approximating minimum manhattan networks in higher dimensions

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

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 ℝ^d , 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 language	English (US)
Title of host publication	Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings
Pages	49-60
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-23719-5_5
State	Published - 2011
Event	19th Annual European Symposium on Algorithms, ESA 2011 - Saarbrucken, Germany Duration: Sep 5 2011 → Sep 9 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6942 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	19th Annual European Symposium on Algorithms, ESA 2011
Country/Territory	Germany
City	Saarbrucken
Period	9/5/11 → 9/9/11

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-23719-5_5

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

Approximating minimum manhattan networks in higher dimensions. / Das, Aparna; Gansner, Emden R.; Kaufmann, Michael et al.
Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings. 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 proceeding › Conference contribution

Das, A, Gansner, ER, 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. 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 S, Spoerhase J, Wolff A. Approximating minimum manhattan networks in higher dimensions. In Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings. 2011. p. 49-60. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-23719-5_5

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AU - Wolff, Alexander

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Approximating minimum manhattan networks in higher dimensions

Abstract

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