Results 1  10
of
229
The multidimensional Manhattan networks
 Siam J. Discrete Math., to appear, http://hdl.handle.net/2117/675. F. Comellas, C. Dalfó and M.A. Fiol
"... Abstract. The ndimensional Manhattan network Mn—a special case of nregular digraph—is formally defined and some of its structural properties are studied. In particular, it is shown that Mn is a Cayley digraph, which can be seen as a subgroup of the ndim version of the wallpaper group pgg. These r ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. The ndimensional Manhattan network Mn—a special case of nregular digraph—is formally defined and some of its structural properties are studied. In particular, it is shown that Mn is a Cayley digraph, which can be seen as a subgroup of the ndim version of the wallpaper group pgg
Approximating a Minimum Manhattan Network
 Nordic J. Comput
, 1999
"... Given a set S of n points in the plane, we dene a Manhattan Network on S as a rectilinear network G with the property that for every pair of points in S, the network G contains the shortest rectilinear path between them. A Minimum Manhattan Network on S is a Manhattan network of minimum possible ..."
Abstract

Cited by 18 (1 self)
 Add to MetaCart
Given a set S of n points in the plane, we dene a Manhattan Network on S as a rectilinear network G with the property that for every pair of points in S, the network G contains the shortest rectilinear path between them. A Minimum Manhattan Network on S is a Manhattan network of minimum
Minimum Manhattan Network is NPComplete
"... A rectilinear path between two points p,q ∈ R 2 is a path connecting p and q with all its line segments horizontal or vertical segments. Furthermore, a Manhattan path between p and q is a rectilinear path with its length exactly dist(p, q): = p.x − q.x  + p.y − q.y. Given a set T of n points in ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
in R 2, a network G is said to be a Manhattan network on T, if for all p, q ∈ T there exists a Manhattan path between p and q with all its line segments in G. For the given point set T, the Minimum Manhattan Network (MMN) Problem is to find a Manhattan network G on T with the minimum network length
Analysis of Bidirectional Manhattan Network with Uplinks
 In Proceedings of the Third International Conference on Computer Communications and Networks
, 1994
"... In this paper we study the effect of introducing additional outofplane links, called "uplinks" to Bidirectional Manhattan Network (BMN). BMN is a twodimensional grid where the nodes of the first and the last row and column of the grid are connected thus forming a torus and where all the ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
In this paper we study the effect of introducing additional outofplane links, called "uplinks" to Bidirectional Manhattan Network (BMN). BMN is a twodimensional grid where the nodes of the first and the last row and column of the grid are connected thus forming a torus and where all
A rounding algorithm for approximating minimum Manhattan networks
 THEOR. COMPUT. SCI
, 2005
"... For a set T of n points (terminals) in the plane, a Manhattan network on T is a network N(T) = (V,E) with the property that its edges are horizontal or vertical segments connecting points in V ⊇ T and for every pair of terminals, the network N(T) contains a shortest l1path between them. A minimu ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
For a set T of n points (terminals) in the plane, a Manhattan network on T is a network N(T) = (V,E) with the property that its edges are horizontal or vertical segments connecting points in V ⊇ T and for every pair of terminals, the network N(T) contains a shortest l1path between them. A
A Simple 3Approximation of Minimum Manhattan Networks
, 2008
"... Given a set P of n points in the plane, a Manhattan network of P is a network that contains a rectilinear shortest path between every pair of points of P. A minimum Manhattan network of P is a Manhattan network of minimum total length. It is unknown whether it is NPhard to construct a minimum Manha ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Given a set P of n points in the plane, a Manhattan network of P is a network that contains a rectilinear shortest path between every pair of points of P. A minimum Manhattan network of P is a Manhattan network of minimum total length. It is unknown whether it is NPhard to construct a minimum
Greedy construction of 2approximation minimum Manhattan network
 IN: PROCEEDINGS OF THE 19TH INTERNATIONAL SYMPOSIUM ON ALGORITHMS AND COMPUTATION
, 2008
"... Given a set T of n points in IR 2, 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 path) of the length exactly the Manhattan distance between p and q. The Minimum Manhattan Network proble ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Given a set T of n points in IR 2, 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 path) of the length exactly the Manhattan distance between p and q. The Minimum Manhattan Network
Polylogarithmic Approximation for Generalized Minimum Manhattan Networks
, 2012
"... Given a set of n terminals, which are points in ddimensional Euclidean space, the minimum Manhattan network problem (MMN) asks for a minimumlength rectilinear network that connects each pair of terminals by a Manhattan path, that is, a path consisting of axisparallel segments whose total length ..."
Abstract
 Add to MetaCart
Given a set of n terminals, which are points in ddimensional Euclidean space, the minimum Manhattan network problem (MMN) asks for a minimumlength rectilinear network that connects each pair of terminals by a Manhattan path, that is, a path consisting of axisparallel segments whose total
Approximating the generalized minimum Manhattan network problem
, 2013
"... 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 minimumlength rectilinear network that connects every pair in R by a Manhattan path, that is, a path of axisparallel ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
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 minimumlength rectilinear network that connects every pair in R by a Manhattan path, that is, a path of axis
Approximating Minimum Manhattan Networks in Higher Dimensions
"... We consider the minimum Manhattan network problem, which is defined as follows. Given a set of points called terminals in R d, find a minimumlength network such that each pair of terminals is connected by a set of axisparallel line segments whose total length is equal to the pair’s Manhattan (tha ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We consider the minimum Manhattan network problem, which is defined as follows. Given a set of points called terminals in R d, find a minimumlength network such that each pair of terminals is connected by a set of axisparallel line segments whose total length is equal to the pair’s Manhattan
Results 1  10
of
229