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Showing papers on "Network topology published in 1990"


Journal ArticleDOI
01 May 1990
TL;DR: Simulation studies show that, given a fixed amount of buffer storage per link, virtual-channel flow control increases throughput by a factor of 3.5, approaching the capacity of the network.
Abstract: Network throughput can be increased by dividing the buffer storage associated with each network channel into several virtual channels [DalSei]. Each physical channel is associated with several small queues, virtual channels, rather than a single deep queue. The virtual channels associated with one physical channel are allocated independently but compete with each other for physical bandwidth. Virtual channels decouple buffer resources from transmission resources. This decoupling allows active messages to pass blocked messages using network bandwidth that would otherwise be left idle. Simulation studies show that, given a fixed amount of buffer storage per link, virtual-channel flow control increases throughput by a factor of 3.5, approaching the capacity of the network.

603 citations


Journal ArticleDOI
F.A. Tobagi1
01 Jan 1990
TL;DR: In this article, three basic types of packet switches are identified: the shared-memory, shared-medium, and space-division types, and a set of definitions and a brief description of the functionality required of fast packet switches is given.
Abstract: Background information on networking and switching is provided, and the various architectures that have been considered for fast packet switches are described. The focus is solely on switches designed to be implemented electronically. A set of definitions and a brief description of the functionality required of fast packet switches are given. Three basic types of packet switches are identified: the shared-memory, shared-medium, and space-division types. Each of these is described, and examples are given. >

463 citations


Patent
15 Feb 1990
TL;DR: In this paper, a wide area communications network (WAN) is defined as a layered network having a hierarchical communications topology, which collects network data generated by a plurality of physical devices such as gas, water or electricity meters.
Abstract: A wide area communications network communicating data from a plurality of network service modules through a plurality of remote cell nodes and intermediate data terminals to a central data terminal. The wide area communications network collects network data generated by a plurality of physical devices such as gas, water or electricity meters, located within a geographical area. The wide area communications network is a layered network having a hierarchical communications topology. The central data terminal controls network operation. Intelligence exists at all layers of the network, thereby easing the workload of the central data terminal. The intelligence attributed to each module is a function of the application of that module.

361 citations


Patent
Lawrence M. Besaw1, Jeff C. Wu1, Cho Y. Chang1, Darren D. Smith1, Mark J. Kean1 
14 May 1990
TL;DR: In this paper, the authors present a system for automatically laying out and graphically displaying the topology of a computer network system, which retrieves a list of the nodes within the network and their interconnections from a database which can be manually built by a network administrator or automatically constructed by other software.
Abstract: A system for automatically laying out and graphically displaying the topology of a computer network system. The layout system retrieves a list of the nodes within the network and their interconnections from a database which can be manually built by a network administrator or automatically constructed by other software. The system will provide any of three views that can be requested by the user. An internet view is the largest and shows the interconnection of different networks. A network view can be shown for any of the networks described in the internet view. A network is comprised of segments and the system will display a view of the nodes connected to any one of the segments. The system will automatically update the view as new nodes become available in the database. This aspect of the system and allows the system to dynamically update the graph when the list of nodes is being supplied by other software. The system also allows the user to dynamically alter the graph by using a graphical input device to move any of the objects displayed on the graph.

269 citations


Journal ArticleDOI
U. Kirsch1
TL;DR: In this paper, the authors studied the problem of singular optimal topologies and showed that the optimal topology might correspond to a singular point in the design space, which is a major obstacle to topological optimization.
Abstract: A major obstacle to topological optimization is that the optimal topology might correspond to a singular point in the design space. Despite its crucial importance, the phenomenon of singular optimal topologies is not well understood.

253 citations


Journal ArticleDOI
TL;DR: A summary is presented of research conducted over the last few years concerning the LAMBDANET multiwavelength optical network, which features full connectivity among the nodes, large nonblocking throughput, data format transparency, and flexible control.
Abstract: A summary is presented of research conducted over the last few years concerning the LAMBDANET multiwavelength optical network. Descriptions are given of some variations, including several applications based on these architectures. Experimental results demonstrate the technological feasibility of this approach. The LAMBDANET design incorporates three basic ingredients: (1) it associates a unique optical wavelength with each transmitting node in a cluster of nodes; (2) the physical topology is that of a broadcast star; and (3) each receiving node identifies transmitting nodes based on the transmission wavelength through wavelength demultiplexing. This network design features full connectivity among the nodes, large nonblocking throughput, data format transparency, and flexible control. The LAMBDANET network is used for both point-to-point and point-to-multipoint applications. >

212 citations


Proceedings ArticleDOI
03 Jun 1990
TL;DR: The fairness problems suffered by distributed-queue-dual-bus (DQDB) networks that span metropolitan areas are examined in detail and a rate control procedure is proposed that requires only a minor modification of the current DQDB protocol.
Abstract: The fairness problems suffered by distributed-queue-dual-bus (DQDB) networks that span metropolitan areas are examined in detail. The problems arise because the network control information is subject to propagation delays that are much longer than the transmission time of a data segment. A rate control procedure is proposed that requires only a minor modification of the current DQDB protocol. In order to guarantee that a node acquires only 90% of the available slots, every time it inserts nine data segments into its local queue it inserts one extra request slot into its transmission queue. This lets an extra idle slot go by that was not requested by any downstream node. >

180 citations


Patent
16 May 1990
TL;DR: In this article, a mesh connected local area network (MCLAN) is proposed to provide automatic packet switching and routing between host computers coupled to the network by point-to-point full duplex links.
Abstract: A mesh connected local area network provides automatic packet switching and routing between host computers coupled to the network. The network has a multiplicity of cut-through, nonblocking switches, each capable of simultaneously routing a multiplicity of data packets. Low host-to-host latency is achieved through the use of cut-through switches with separate internal buffers for each packet being routed. The switches are interconnected with one another and are coupled to the host computers of the network by point to point full duplex links. While each switch can be coupled to ten or more network members, i.e., switches and hosts, each link is coupled to only two network members and is dedicated to carrying signals therebetween. Whenever a new switch or link is added to the network, and whenever a switch or link fails, the switches in the network automatically reconfigure the network by recomputing the set of legal paths through the network.

174 citations


Book ChapterDOI
24 Sep 1990
TL;DR: A self stabilizing protocol for constructing a rooted spanning tree in an arbitrary asynchronous network of processors that communicate through shared memory is presented.
Abstract: A self stabilizing protocol for constructing a rooted spanning tree in an arbitrary asynchronous network of processors that communicate through shared memory is presented. The processors have unique identifiers but are otherwise identical. The network topology is assumed to be dynamic, that is, edges can join or leave the computation before it eventually stabilizes.

153 citations


Proceedings ArticleDOI
03 Jun 1990
TL;DR: The problems of virtual- and physical-topology design in the WON are described, techniques for their solution are presented, and the interplay between these problems is studied.
Abstract: The twofold purpose of this research is to develop mathematical programming tools for the optimal or near-optimal design of a new type of network architecture called the wavelength-division optical network (WON) and to discover underlying design principles for such networks via experimentation using these tools. The WON, a multichannel, multihop lightwave network with tunable transceivers, is suitable for use as a metropolitan area network. A unique feature of the WON is that a great number of virtual topologies can be mapped onto a given physical topology. The problems of virtual- and physical-topology design in the WON are described, techniques for their solution are presented, and the interplay between these problems is studied. >

146 citations


Patent
30 Jan 1990
TL;DR: In this paper, the authors propose a tree-expansion scheme for tree topologies, which allows arbitrary up-sizing of the PE count to build virtually any size of tree network, with each size exhibiting same high degree of fault tolerance and reconfigurability.
Abstract: An interconnection scheme among the processing elements ("PEs") of a multiprocessor computing architecture realizes, through PE reconfiguration, both fault tolerance and a wide variety of different processing topologies including binary trees and linear systolic arrays. By using a novel variant on a tree expansion scheme, the invention also allows for arbitrary up-sizing of the PE count to build virtually any size of tree network, with each size exhibiting same high degree of fault tolerance and reconfigurability. The invention may be practiced with 4-port PEs arrayed in a module comprising a 4×4 board-mounted PE lattice. Each PE has four physical ports, which connect to the similar ports of its lattice neighbors. Each PE has an internal capability to be configured to route signals to or from any of its neighbors. Thus, for tree topologies, any of the four neighbors of a given PE may be selected as the parent of the given PE; and any or all of the remaining three neighboring PEs may be selected as the child(ren) PEs. The PE ports are configured under the control of a remote host, which establishes an initial desired PE topology. The operability of the PEs is tested, and information on faulty PEs or communications paths is used to enable or disable nodes as necessary by revising the PE port configurations. The nodes thus are reorganized and can run or continue running, on a degraded basis.

Journal ArticleDOI
TL;DR: It is shown that the message complexity of broadcast depends on the exact complexity measure, and it is proved that, if one counts messages of bounded length, then broadcast requires &THgr;(↿E
Abstract: This paper concerns the message complexity of broadcast in arbitrary point-to-point communication networks. Broadcast is a task initiated by a single processor that wishes to convey a message to all processors in the network. The widely accepted model of communication networks, in which each processor initially knows the identity of its neighbors but does not know the entire network topology, is assumed. Although it seems obvious that the number of messages required for broadcast in this model equals the number of links, no proof of this basic fact has been given before.It is shown that the message complexity of broadcast depends on the exact complexity measure. If messages of unbounded length are counted at unit cost, then broadcast requires T(uVu) messages, where V is the set of processors in the network. It is proved that, if one counts messages of bounded length, then broadcast requires T(uEu) messages, where E is the set of edges in the network.Assuming an intermediate model in which each vertex knows the topology of the network in radius r ≥ 1 from itself, matching upper and lower bounds of T(min{uEu, uVu1+T(l)/r}) is proved on the number of messages of bounded length required for broadcast. Both the upper and lower bounds hold for both synchronous and asynchronous network models.The same results hold for the construction of spanning trees, and various other global tasks.

Patent
27 Mar 1990
TL;DR: In this paper, a controller broadcasts a series of polling frames to all terminals, the response to each of which is a single bit (pulse) from any terminal remaining eligible to respond.
Abstract: Tis method provides high utilization collision free access to a digital pulse communications medium with priority provided by message class and/or terminal type, regardless of network topology. This is accomplished by utilizing a controller which broadcasts a series of polling frames to all terminals, the response to each of which is a single bit (pulse) from any terminal remaining eligible to respond. All responses to a poll are logically OR'ed by the network to provide a combined response frame at the controller, thus making the process ambivalent to collisions. A polling frame and associated response frame, called a polling cycle, determines one digit of a selected address. A terminal not selected in a given cycle is blocked from responding further, until its high order digit(s) are again selected. Each polling cycle is therefore context sensitive, thus maximizing the information flow per poll and minimizing data flow and network travel time per terminal selection. Each polling frame specifies the value of the address digit being tested, thereby giving the controller complete control of priority of network addresses to receive service. To provide priority by message class, the additional message class bits are prefixed to each terminal address, providing a unique address for each terminal/message class combination. Each terminal is then free to modify the prefix of its own address to specify message priority.

Proceedings ArticleDOI
17 Jun 1990
TL;DR: The key innovation is the representation of neuron activations and synaptic weights as stochastic functions of time, leading to efficient implementations of the synapses, and a flexible architecture that permits the realization of arbitrary network topologies and dimensions.
Abstract: An approach to solving the two most serious shortcomings of previous artificial neural network implementations is discussed. A flexible architecture that permits the realization of arbitrary network topologies and dimensions is presented. Furthermore, the performance of this architecture is independent of the size of the network and permits the processing of typically 100000 patterns per second. The key innovation is the representation of neuron activations and synaptic weights as stochastic functions of time, leading to efficient implementations of the synapses. High densities of synapses per silicon area, exceeding even analog implementations, have been achieved. Finally, the neuron activations are represented digitally, as are the synaptic computations, thereby permitting fabrication of digital neural network architectures using a variety of standard, low-cost semiconductor processes. A pair of general-purpose chips (SU3232 and NU32) that permit post facto construction of neural networks of arbitrary topology and virtually unlimited dimensions is presented

Journal ArticleDOI
TL;DR: A clock synchronization scheme that strikes a balance between hardware and software solutions is proposed, and the guaranteed worst-cast skews can be made insensitive to the maximum variation of message transit delay in the system.
Abstract: A clock synchronization scheme that strikes a balance between hardware and software solutions is proposed. The proposed scheme is a software algorithm that uses minimal additional hardware to achieve reasonably tight synchronization. Unlike other software solutions, the guaranteed worst-cast skews can be made insensitive to the maximum variation of message transit delay in the system. The scheme is particularly suitable for large partially connected distributed systems with topologies that support simple point-to-point broadcast algorithms. Examples of such topologies include the hypercube and the mesh interconnection structures. >

Patent
Steven F. Nugent1
27 Dec 1990
TL;DR: In this paper, the authors propose an adaptive routing means and method useful for transferring messages on a number of multi-dimensional network topologies that connect distributed multi-processing systems, where messages are routed in networks A and B by routing first in the X dimension and then in the Y dimension.
Abstract: An adaptive routing means and method useful for transferring messages on a number of multi-dimensional network topologies that connect distributed multi-processing systems. A plurality of processing nodes comprising processing means for processing information and router means for routing messages are connected in a multi-dimensional network (A) with an identical or redundant message passing multi-dimensional network (B) of routers being connected to network A. Each router comprises four types of channels for message passing: 1) a channel to transfer information between a router and a processor coupled to the router, 2) a channel to transfer information in an X direction, 3) a channel for the Y direction, and 4) a channel for the Z direction. This connectivity allows messages to pass between nodes within network A, between routers within network B, or between network A and network B by passing through a router. Messages are routed in networks A and B by routing first in the X dimension and then in the Y dimension. The present invention transitions between A and B networks when contention is encountered in the X or Y direction, if the appropriate Z channel is available. If an X or Y channel is not immediately granted, a request is made for the Z channel. Both the request for an X or Y channel and the request for the Z channel are maintained until one request is granted. The message is then routed on the granted channel and the other request is withdrawn. The router does not commit to routing on a particular channel until one channel is available.

Journal ArticleDOI
TL;DR: Four algorithms are developed to determine the exact blocking probability for each of the classes in a circuit-switched network consisting of multiple-access links connected to a common link.
Abstract: A circuit-switched network consisting of multiple-access links connected to a common link is considered. Each call requires circuits on one access link and on the common link. The network supports multiple classes of calls where each class specifies a bandwidth requirement, an arrival rate, and a holding-time distribution. Based on a product-form solution for these networks, four algorithms are developed to determine the exact blocking probability for each of the classes. The first two algorithms are based on convolution, the third on the fast Fourier transform, and the fourth on a recursion due to J.S. Kaufman (1981) and to J.W. Roberts (1981). Complexity bounds and numerical results demonstrate that these algorithms can determine blocking probabilities in reasonable CPU time for networks with thousands of circuits. >

Proceedings ArticleDOI
24 Jun 1990
TL;DR: It is shown that there exists a pseudo-polynomial time algorithm for finding the optimal solution to the problem of choosing the proper sizes from a cell library for the logic elements of a Boolean network to meet timing constraints on the propagation delay.
Abstract: Examined is a problem of choosing the proper sizes from a cell library for the logic elements of a Boolean network to meet timing constraints on the propagation delay along every path from the primary input to the primary output. It is shown that, if the Boolean network has a tree topology, there exists a pseudo-polynomial time algorithm for finding the optimal solution to this problem. A backtracking-based algorithm for finding feasible solutions for networks that are not trees is also suggested and evaluated. >

Proceedings ArticleDOI
T.E. Stern1
02 Dec 1990
TL;DR: A novel type of lightwave network architecture that is based on establishing controllable, optically transparent paths among network users is described, and is capable of being reconfigured in response to changing load conditions or component failures.
Abstract: A novel type of lightwave network architecture that is based on establishing controllable, optically transparent paths among network users is described. The objective is to provide optical connections on demand. These connections would support a high degree of flexibility, including user-chosen modulation formats and bit rates, for large numbers of user stations (e.g., 100000) using mesh-type topologies that are spread over geographical areas that may extend to diameters of several thousand kilometers. The networks in question perform only linear operations on optical signals, essentially operating as a dynamically controlled 'ether' within which light beams are selectively directed between prescribed source-destination pairs. Because these linear lightwave networks are controllable, they are capable of being reconfigured in response to changing load conditions or component failures. >

Journal ArticleDOI
TL;DR: The distribution of galaxies in the universe displays a rich structure and information not contained in the power spectrum can be obtained from the topology of the distribution as mentioned in this paper, which is related to the connectivity by the Gauss-Bonnet theorem.

Journal ArticleDOI
U. Kirsch1
TL;DR: In this paper, the relationship between two optimal design problems is investigated: (a) the fixed geometry problem, where the topology is optimized for a predetermined geometry, and (b) the geometries of multiple optimal topologies are studied.
Abstract: The relationship between two optimal design problems is investigated: (a) The fixed geometry problem, where the topology is optimized for a predetermined geometry. (b) The fixed topology problem, where the geometry is optimized for a given topology. Assuming approximate linear programming formulations, conditions of optimality are derived and geometries of multiple optimal topologies are studied. Some considerations related to a general design procedure for optimization of topology, geometry and cross-sections are discussed.

Proceedings ArticleDOI
03 Jun 1990
TL;DR: Diversity coding can be extended to provide protection from short-duration environmental disruptions, such as multipath fading in radio networks and polarization dispersion in fiber-optic networks, or, in conjunction with previous error detection schemes, to provide forward error correction for random and burst errors.
Abstract: An error-control-based approach, called diversity coding, that provides nearly instantaneous self-healing digital communication networks is presented. This is achieved by constructing an error-correcting code across logically independent channels and by treating link failures within the framework of an erasure channel model. Diversity coding is more efficient than previous approaches to self-healing communication networks since it is nearly instantaneous, is transparent to the end user, minimizes the required extra capacity, and does not need rerouting, resynchronization, or a feedback channel. It is applicable to both circuit-switched and packet-switched networks and to a wide variety of network topologies. Diversity coding can be extended to provide protection from short-duration environmental disruptions, such as multipath fading in radio networks and polarization dispersion in fiber-optic networks, or, in conjunction with previous error detection schemes, to provide forward error correction for random and burst errors. >

Journal ArticleDOI
TL;DR: Simulation results for a pulse-code modulation (PCM) voice encoder, a sigma-delta modulator, a neural network, and a phase-locked loop are presented to demonstrate the flexibility of the signal-dependent modification of network topology.
Abstract: The simulation of mixed switched-capacitor/digital (SC/D) networks containing capacitors, independent and linear-dependent voltage sources, switches controlled either by periodic or nonperiodic Boolean signals, latched comparators, and logic gates is considered. A unified linear switched-capacitor network (SCN) and mixed SC/D network simulator, SWITCAP2, and its applications to several widely used and novel nonlinear SCNs are discussed. The switches may be controlled by periodic waveforms and by nonperiodic waveforms from the outputs of comparators and logic gates. The signal-dependent modification of network topology through the comparators, logic gates, and signal-driven switches makes the modeling of various nonlinear switched-capacitor circuits possible. Simulation results for a pulse-code modulation (PCM) voice encoder, a sigma-delta modulator, a neural network, and a phase-locked loop (PLL) are presented to demonstrate the flexibility of the approach. >

Proceedings ArticleDOI
03 Jun 1990
TL;DR: The proposed lightpath architecture trades the ample bandwidth obtained by using multiple wavelengths for a reduction in the number of processing stages and a simplification of each switching stage, leading to substantially increased throughput.
Abstract: An inherent problem of conventional point-to-point wide area network (WAN) architectures is that they cannot translate optical transmission bandwidth into comparable user-available throughput due to the limiting electronic processing speed of the switching nodes. A solution to wavelength division multiplexing (WDM)-based WAN networks that addresses this limitation is presented. The proposed lightpath architecture trades the ample bandwidth obtained by using multiple wavelengths for a reduction in the number of processing stages and a simplification of each switching stage, leading to substantially increased throughput. The principle of the lightpath architecture is the construction and use of a virtual topology network in the wavelength domain, embedded in the original network. A study is made of the embedding of virtual networks whose topologies are regular, using algorithms which provide bounds on the number of wavelengths, switch sizes, and average number of switching stages per packet transmission. >

Patent
19 Sep 1990
TL;DR: In this paper, a method and apparatus for detecting invalid network topologies in a local area network (LAN) is presented, where the stations comprising the LAN include single attachment stations, dual attachment stations (DAS), wire concentrators (WC), and DAS/WC combination stations.
Abstract: A method and apparatus for detecting invalid network topologies in a local area network (LAN). The stations comprising the LAN include single attachment stations (SAS), dual attachment stations (DAS), wire concentrators (WC), and DAS/WC combination stations. Adjacent stations exchange connection type information identifying a type of physical connection of the station sending the connection information. A station receiving the connection information determines whether the connection is valid for its physical connection type using a connection matrix. Invalid connections can result in a network topology where stations are physically connected, but are not logically connected, because the stations do not all form a primary ring. Invalid connections may be rejected and bypassed in each station. Alternately, a station detecting an invalid connection may reconfigure itself using an internal data switch. The actions of each station, taken together, achieve a globally designated primary ring.

Journal ArticleDOI
01 Sep 1990
TL;DR: It is shown that among the different classical processors networks topologies (ring, 2d-torus or n-cube), the hypercube topology minimizes the communications.
Abstract: This paper introduces the parallelization on a distributed memory multicomputer of two iterative methods for finding all the roots of a given polynomial. The parallel algorithms share the computation of the roots among the processors and perform a total exchange of the data at each step. Since the amount of communications is the main drawback of this approach, we study the effect of the network topology on the performance of the algorithms. Particularly, we show that among the different classical processors networks topologies (ring, 2d-torus or n-cube), the hypercube topology minimizes the communications. For each topology is computed the optimal number of processors. Experiments on the hypercube FPS T40 illustrate the results.

Proceedings ArticleDOI
22 Oct 1990
TL;DR: It is shown that keeping track of history allows significant improvements in the realistic model of communication complexity of dynamic network protocols, and it is found that amortized communication complexity, i.e. incremental cost of adapting to a single topology change, can be smaller than the communications complexity of solving the problem from scratch.
Abstract: It is shown that keeping track of history allows significant improvements in the realistic model of communication complexity of dynamic network protocols. The communication complexity for solving an arbitrary graph problem is improved from Theta (E) to Theta (V), thus achieving the lower bound. Moreover, O(V) is also the amortized complexity of solving an arbitrary function (not only graph functions) defined on the local inputs of the nodes. As a corollary, it is found that amortized communication complexity, i.e. incremental cost of adapting to a single topology change, can be smaller than the communication complexity of solving the problem from scratch. The first stage in the solution is a communication-optimal maintenance of a spanning tree in a dynamic network. The second stage is the optimal maintenance of replicas of databases. An important example of this task is the problem of updating the description of the network's topology at every node. For this problem the message complexity is improved from O(EV) to Theta (V). The improvement for a general database is even larger if the size of the database is larger than E. >

Proceedings ArticleDOI
05 Feb 1990
TL;DR: The problem of properly scheduling data transfers in order to complete this redistribution process in minimum possible time is investigated and a useful upper bound for optimal solutions is presented.
Abstract: In a distributed database system there is a need for periodic changes in data distribution due to such factors as changes in query patterns and network topology. A proper redistribution of data is necessary to provide acceptable system performance, as measured by the average execution time of transactions. The problem of properly scheduling data transfers in order to complete this redistribution process in minimum possible time is investigated. This problem takes into account the constraints on communication resources of the system. The complexity of the problem is discussed, and a useful upper bound for optimal solutions is presented. Also given are procedures for finding optimal and approximate solutions to this problem. >

Journal ArticleDOI
TL;DR: The authors present a set of techniques that can be used to identify and quickly solve three characteristic network configurations: trees, simple loops, and series resistors with interspersed current sources.
Abstract: Analysis of power distribution in VLSI circuits requires the solution of a large network of resistors and current sources. Fortunately, these resistor networks have certain characteristic properties that permit partitioning into smaller, easier to solve sections. The authors present a set of techniques that can be used to identify and quickly solve three characteristic network configurations: trees, simple loops, and series resistors with interspersed current sources. Methods for efficiently solving other sections of the network are also explored. System performance of several designs is reported. >

Journal ArticleDOI
01 Mar 1990-Networks
TL;DR: A generalization of the ring network by adding two fixed-step links to each node is considered, which has low diameter, easy routing, and switching structure and therefore is suitable for implementation in the design of reliable networks.
Abstract: The problem under consideration arises from studies on local networks and multimodule memory organizations. The ring network has been one of the popular network topologies used in the design and implementation of local area networks and other configurations. We consider here a generalization of the ring network by adding two fixed-step links to each node. The resulting networks have low diameter, easy routing, and switching structure and therefore are suitable for implementation in the design of reliable networks. Let N denote the number of nodes in the network. For a given N, we are concerned with the problem of determining the best topologies to minimize the diameter (and, hence, the transmission delay) of the network. We obtain new classes of values of N for which topologies can be found that achieve the lower bound lb = [(√2N - 1 - 1)/2] for the minimum diameter. We also show that for some infinite classes of N this lower bound lb is not achievable.