Showing papers on "Node (networking) published in 1968"

Minimum Concave Cost Flows in Certain Networks

Abstract: The literature is replete with analyses of minimum cost flows in networks for which the cost of shipping from node to node is a linear function. However, the linear cost assumption is often not realistic. Situations in which there is a set-up charge, discounting, or efficiencies of scale give rise to concave functions. Although concave functions can be minimized by an exhaustive search of all the extreme points of the convex feasible region, such an approach is impractical for all but the simplest of problems. In this paper some theorems are developed which explicitly characterize the extreme points for certain single commodity networks. By exploiting this characterization algorithms are developed that determine the minimum concave cost solution for networks with a single source and a single destination, for acyclic single source multiple destination networks, and for acyclic single destination multiple source networks. An interesting theorem then establishes that for either single source or single destination networks the multi-commodity case can be reduced to the single commodity case. Applications to the concave warehouse problem, a single product production and inventory model, a multi-product production and inventory model, and a plant location problem are included.

Permutation procedure for minimising the number of crossings in a network

Abstract: The paper describes a method for laying out networks by computer so that the number of crossings between the network connections is close to a minimum. The problem is relevant to the design of printed circuits, where special wiring arrangements have to be made when crossings occur. The network is expressed in the form of a permutation, which is convenient for manipulation, by deforming the network so that the node points lie on a straight line with the connections drawn as semicircles above an below the node line. Locally optimal networks are defined so that no gain can result from moving an individual node to a new position, and a 2-stage method of construction is proposed. The formulas used to calculate the number of crossings consist primarily of summations, so that the procedure is quickly performed on a computer. The method has been tested on some trial networks for which the minimum number of crossings is known, and it has also been compared with Monte Carlo methods on random networks. The results are encouraging in all cases.

A comparative investigation of the computational efficiency of shortest path algorithms

Abstract: : Efficiency of shortest path algorithms is a function of various network parameters. This paper reports the results of an investigation of five algorithms for finding the shortest path from a root node to all other nodes for different network structures. Parameters considered are number of nodes, number of links, range of data (i.e., arc lengths), and shape (if applicable). It is hoped that the results will suggest to potential users of these algorithms which one is best suited for their problem.

Maximizing flow through a network with node and arc capacities

Abstract: In many actual network flow situations, nodes as well as arcs have limited capacities. This paper presents, for such a network, an algorithm for maximizing flow from a source node to a sink node. The algorithm allows us to treat these situations without introducing artificial arcs and nodes, as has been done in the past. Eliminating the artificial arcs and nodes simplifies network analysis since it always results in half as many nodes, as well as less than half as many arcs if the original arcs are undirected. In addition, the following generalization of Ford and Fulkerson’s max-flow, min-cut theorem is presented and proven. Consider two subsets of the nodes, X and Y, whose union is the set of all network nodes and such that the source node is a member of X, and the sink node is a member of Y. Then, forming a cut set separating the source and sink are the nodes in the intersection of X and Y, and the set of all arcs (i, j), such that i is a member of X − Y, and j is a member of Y − X. Letting a cut set's ...

Synthesis of a Class of n-Port Networks

Abstract: The properties of a class of 2n -node networks, called K -networks, are discussed. The characteristic of a K -network is that when any one of its ports is connected to a voltage source keeping all the other ports short circuited, then all the short-circuited ports are at the same potential. The 2n -node network with a pair of equal conductances joining any two ports, as obtained by the presently known procedure for the realization of a dominant conductance matrix, is shown to be a special structure belonging to this general class. It is shown that the realization of a real dominant matrix as the short-circuit conductance matrix Y of an n -port network can be convenientlycarried out using K -networks. Further, the "modified cut-set matrix" of a K -network is of a special form, independent of edge conductances. This property can be made use of in generating a range of equivalent 2n -node n -port networks for a given Y . Examples illustrating the realization procedures are included.