Permutation pattern-avoidance is a central concept of both enumerative and extremal
combinatorics. In this paper we study the effect of permutation pattern-avoidance on the …

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 …

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 …

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 …

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 …

We study the generalized minimum Manhattan network (GMMN) problem: given a set PP of
pairs of points in the Euclidean plane R^ 2 R 2, we are required to find a minimum-length …

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 …

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 …

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 …

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 …