Abstract
We study the generalized minimum Manhattan network (GMMN) problem: given a set \(P\) of pairs of points in the Euclidean plane \(\mathbb R^2\), we are required to find a minimum-length geometric network which consists of axis-aligned segments and contains a shortest path in the \(L_1\) metric (a so-called Manhattan path) for each pair in \(P\). This problem commonly generalizes several NP-hard network design problems that admit constant-factor approximation algorithms, such as the rectilinear Steiner arborescence (RSA) problem, and it is open whether so does the GMMN problem.
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