Minimum Manhattan network is NP-complete

FYL Chin, Z Guo, H Sun - Proceedings of the twenty-fifth annual …, 2009 - dl.acm.org
A rectilinear path between two points p, q∈ R2 is a path connecting p and q with all its line
segments horizontal or vertical segments. Furthermore, a Manhattan path between p and q …

Approximating the generalized minimum Manhattan network problem

A Das, K Fleszar, S Kobourov, J Spoerhase… - Algorithmica, 2018 - Springer
We consider the generalized minimum Manhattan network problem (GMMN). The input to
this problem is a set R of n pairs of terminals, which are points in R^ 2 R 2. The goal is to find …

Approximating minimum Manhattan networks in higher dimensions

A Das, ER Gansner, M Kaufmann, S Kobourov… - Algorithmica, 2015 - Springer
We study the minimum Manhattan network problem, which is defined as follows. Given a set
of points called terminals in R^d, find a minimum-length network such that each pair of …

[PDF][PDF] The generalized minimum Manhattan network problem (GMMN)–scale-diversity aware approximation and a primal-dual algorithm

S Funke, MP Seybold - Proceedings of Canadian Conference on …, 2014 - cccg.ca
In the d-dimensional Generalized Minimum Manhattan Network (d-GMMN) problem one is
interested in finding a minimum cost rectilinear network N connecting a given set R of n pairs …

A Simple 2-Approximation Algorithm For Minimum Manhattan Network Problem

MMR Sanim, S Saira, FF Ahsan, R Bardhan… - arXiv preprint arXiv …, 2024 - arxiv.org
Given an points in two dimensional space, a Manhattan Network G is a network that
connects all n points with either horizontal or vertical edges, with the property that for any …

Greedy construction of 2-approximate minimum Manhattan networks

Z Guo, H Sun, H Zhu - International Journal of Computational …, 2011 - World Scientific
Given a set T of n points in ℝ2, a Manhattan network on T is a graph G=(V, E) with the
property that all the edges in E are vertical or horizontal line segments connecting points in …

A fixed-parameter algorithm for the minimum Manhattan network problem

C Knauer, A Spillner - Journal of Computational Geometry, 2011 - jocg.org
A Manhattan network for a finite set P of points in the plane is a geometric graph such that its
vertex set contains P, its edges are axis-parallel and non-crossing and, for any two points p …

The Rectilinear Steiner Forest Arborescence problem

Ł Mielewczyk, L Palios, P Żyliński - arXiv preprint arXiv:2210.04576, 2022 - arxiv.org
Let $ r $ be a point in the first quadrant $ Q_1 $ of the plane $\mathbb {R}^ 2$ and let $
P\subset Q_1 $ be a set of points such that for any $ p\in P $, its $ x $-and $ y $-coordinate is …

Approximating the generalized minimum Manhattan network problem

A Das, K Fleszar, S Kobourov, J Spoerhase… - … and Computation: 24th …, 2013 - Springer
We consider the generalized minimum Manhattan network problem (GMMN). The input to
this problem is a set R of n pairs of terminals, which are points in ℝ 2. The goal is to find a …

Polylogarithmic approximation for generalized minimum manhattan networks

A Das, K Fleszar, S Kobourov, J Spoerhase… - arXiv preprint arXiv …, 2012 - arxiv.org
Given a set of $ n $ terminals, which are points in $ d $-dimensional Euclidean space, the
minimum Manhattan network problem (MMN) asks for a minimum-length rectilinear network …