The rectilinear Steiner arborescence problem is NP-complete
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
An Improved Algorithm for the Minimum Manhattan Network Problem
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Approximating a minimum Manhattan network
Nordic Journal of Computing
A rounding algorithm for approximating minimum Manhattan networks
Theoretical Computer Science
The minimum Manhattan network problem: Approximations and exact solutions
Computational Geometry: Theory and Applications
A 1.5-approximation of the minimal manhattan network problem
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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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@?PxP of pairs. The complexity status of the MMN problem is still unsolved in =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 (Transitive Minimum Manhattan Subnetwork (TMMSN) Problem) and show that the TMMSN problem in 3 dimensions is NP-complete.