Showing papers on "Connectivity published in 1983"

Distributed task and memory management

Abstract: A model of distributed graph reduction is described that has features common to many distributed computing systems: a program (represented as a graph) is partitioned and dynamically distributed among an arbitrary number of processing elements having only local store, and computation takes place as tasks are propagated between vertices in the graph. Specific problems are addressed that are inherent in a computing model of this sort, including garbage collection, detecting deadlock, deleting tasks, and the dynamic prioritization of tasks. By characterizing these problems in terms of graph connectivity, a decentralized graph-marking algorithm is shown to provide an effective solution. This algorithm is unique in that it allows marking a distributed graph whose connectivity is continually changing.

Statistical disorder and the analysis of a communication‐graph

Abstract: The lines of a co-author graph represent channels of communication through which information has been and may continue to be informally exchanged. The Brillouin Information Measure can be used to describe important properties of the co-author graph and other communication-graphs. The “connectedness” of a graph can be represented on a scale in which one limiting value signifies a connected graph and the other limiting value signifies a graph in which all points are isolated. Important points can be distinguished from all other points in a communication-graph. These important points are defined mathematically and are called synthetic cutpoints. A measure of importance can be assigned to each point in a communication-graph. This measure can be used to order points in terms of their contribution to a favorable communication-structure.

Ramsey theory for graph connectivity

Abstract: rc(k) Denotes the smallest integer such that any c-edge-coloring of the rc(k) vertex complete graph has a monochromatic k-connected subgraph. For any c, k ≧ 2, we show 2c(k – 1) + 1 ≦ rc(k) < 10/3 c(k – 1) + 1, and further that 4(k – 1) + 1 ≧ r2(k) < (3 + √ (k – 1) + 1. Some exact values for various Ramsey connectivity numbers are also computed.

On the Connectivity of Some Telecommunications Networks

Abstract: Memmi and Raillard constructed two families of graphs, regular of degree d and diameter k which are useful for designing telecommunications networks ([(d, k) graph problem]). They conjectured that the connectivity of these graphs were equal to their degree. We prove here these conjectures, that implies that the networks have the best possible reliability.

Graph theoretical approach to a highly reliable network

Abstract: This paper presents a method of constructing a highly reliable and efficient communication network using two types of directed graphs called “extended complete graph (ECG)” and “quasi-ECG.” They are nearly minimum in diameter and nearly maximum in connectivity for any number of nodes. These graphs are evaluated for diameter, connectivity and “vulnerability” which is defined to represent the throughput deterioration caused by network constituent failure. A network constructed using (quasi-) ECGs is also shown to be comparative to the commercial network in the mean value of transit switching stages per call.

Application of the minimum-weight spanning-tree algorithm to assignment of communication facilities

Abstract: COSMOS — the Computer System for Main Frame Operations — is an operational support system that inventories and assigns central office facilities to serve customer circuits As part of this assignment responsibility, COSMOS must provide the central office personnel who will physically connect the circuit not only with information about the facilities to be connected, but also the order in which they will be connected (ie, connection sequence or “connectivity”) Also, COSMOS must determine the circuit connectivity to permit automatic assignment of tie pairs — inter- and intra-frame cables that permit the connection of facilities that are widely separated physically A new algorithm has been added to COSMOS to permit the determination of connectivity This algorithm is based on the algorithm that determines the minimum-weight spanning tree of a connected graph However, the algorithm is specialized for COSMOS by taking into account such factors as minimizing the maximum number of connections at any node and restricting certain nodes to a maximum number of connections