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. 298307.
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 1spanner 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 MaxSNP complete with epsilon<frac{1}{8} in 3 dimensions.
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Item Type:  Article 

Citations:  2 (Google Scholar)  0 (Web of Science) 
Uncontrolled Keywords:  1spanner 3 dimensions grid graph manhattan network 
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Divisions:  Institute of Computer Science > Computer Science Department  Prof. Dr. Schrader Mathematical Institute > Prof. Dr. Faigle 
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ZAIK Number:  zaik2008577 

Depositing User:  Birgit Engels 
Date Deposited:  17 May 2011 00:00 
Last Modified:  19 Dec 2011 09:44 
URI:  http://earchive.informatik.unikoeln.de/id/eprint/577 