Approximating Minimum Manhattan Networks in Higher Dimensions release_64b4lnvq65gvrbcw2ienjb5riu

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

Released as a article .

2012  

Abstract

We study the minimum Manhattan network problem, which is defined as follows. Given a set of points called terminals in ^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 >0, an O(n^)-approximation algorithm. For 3D, we also give a 4(k-1)-approximation algorithm for the case that the terminals are contained in the union of k > 2 parallel planes.
In text/plain format

Archived Files and Locations

application/pdf  516.8 kB
file_fqmieuhhy5fzjfsnn7fjcqjize
archive.org (archive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2012-04-27
Version   v2
Language   en ?
arXiv  1107.0901v2
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: e9035fe0-fb8d-40d6-9502-061b18465a55
API URL: JSON