Universität zu Köln

Engels, Birgit (2010). The Transitive Minimum Manhattan Subnetwork Problem in 3 Dimensions. Discrete Applied Mathematics, 158 (4). pp. 298-307. Elsevier Science.

Preview

PDF zaik2008-577.pdf - Submitted Version Download (260kB) | Preview

Abstract

We consider the Minimum Manhattan Subnetwork (MMSN) Problem which generalizes the already known Minimum Manhattan Network (MMN) Problem: Given a set P of n points in the plane, find shortest rectilinear paths between all pairs of points. These paths form a network, the total length of which has to be minimized. From a graph theoretical point of view, a MMN is a 1-spanner with respect to the L_1 metric. In contrast to the MMN problem, a solution to the MMSN problem does not demand L_1 -shortest paths for all point pairs, but only for a given set R subseteq P imes P of pairs. The complexity status of the MMN problem is still unsolved in geq 2 dimensions, whereas the MMSN was shown to be NP -complete considering general relations R in the plane. We restrict the MMSN problem to transitive relations R_T ({em Transitive} Minimum Manhattan Subnetwork (TMMSN) Problem) and show that the TMMSN problem is Max-SNP -complete with epsilon<frac{1}{8} in 3 dimensions.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Engels, Birgit UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-549786
Journal or Publication Title:	Discrete Applied Mathematics
Series Name:	Discrete Applied Mathmatics
Volume:	158
Number:	4
Page Range:	pp. 298-307
Date:	2010
Publisher:	Elsevier Science
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Institute of Computer Science
Subjects:	Data processing Computer science
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/54978