Given a set P of n points with their pairwise distances, the traveling salesman problem (TSP)
asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when …

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 …

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 …

Given a set T of n points in, a Manhattan Network G is a network with all its edges horizontal
or vertical segments, such that for all p, q∈ T, in G there exists a path (named a Manhattan …

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 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 …

An important problem that commonly arises in areas such as internet traffic-flow analysis,
phylogenetics and electrical circuit design, is to find a representation of any given metric D …

We consider minimum-cardinality Manhattan connected sets with arbitrary demands: Given
a collection of points P in the plane, together with a subset of pairs of points in P (which we …

In this paper we address the Minimum Manhattan Network (MMN) problem. It is an important
geometric problem with vast applications. As it is an NP-complete discrete combinatorial …

Let B be a centrally symmetric convex polygon of ℝ 2 and‖ p− q‖ be the distance between
two points p, q∈ ℝ 2 in the normed plane whose unit ball is B. For a set T of n points …