TY - GEN

T1 - Approximating minimum manhattan networks in higher dimensions

AU - Das, Aparna

AU - Gansner, Emden R.

AU - Kaufmann, Michael

AU - Kobourov, Stephen

AU - Spoerhase, Joachim

AU - Wolff, Alexander

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-642-23719-5_5

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

M3 - Conference contribution

AN - SCOPUS:80052801807

SN - 9783642237188

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 49

EP - 60

BT - Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings

T2 - 19th Annual European Symposium on Algorithms, ESA 2011

Y2 - 5 September 2011 through 9 September 2011

ER -