The Transitive Minimum Manhattan Subnetwork Problem in 3 Dimensions

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

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.


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Deposit Information:
ZAIK Number: zaik2008-577
Depositing User: Birgit Engels
Date Deposited: 17 May 2011 00:00
Last Modified: 19 Dec 2011 09:44
URI: http://e-archive.informatik.uni-koeln.de/id/eprint/577