Multicommodity flows in tree-like networks

A problem of finding multicommodity minimum-cost flows in tree-like networks is considered. To solve this problem, an algorithm based on the reduction to a problem of finding a single-commodity flow in a network of arbitrary structure is proposed. For single-commodity flows in tree-like networks, an algorithm using a procedure of border reduction is used.     

Topology optimization of interconnection networks

This paper describes an automatic optimization tool that searches a family of network topologies to select the topology that best achieves a specified set of design goals while satisfying specified packaging constraints. Our tool uses a model of signaling technology that relates bandwidth, cost and distance of links. This model captures the distance-dependent bandwidth of modern high-speed electrical links and the cost differential between electrical and optical links. Using our optimization tool, we explore the design space of hybrid Clos-torus (C-T) networks. For a representative set of packaging constraints we determine the optimal hybrid C-T topology to minimize cost and the optimal C-T topology to minimize latency for various packet lengths. We then use the tool to measure the sensitivity of the optimal topology to several important packaging constraints such as pin count and critical distance.     

Equivalence relations among interconnection networks

The interconnection network equivalence notions reported in the literature are formalized via conjugation maps over the sets of interconnections of such networks. Various forms of relations including group isomorphisms among interconnection networks are introduced. Equivalence relations express the degrees of freedom in “making one network behave like another.” Examples of these relations for commutative cube-connected networks with individual stage control are also included. In addition, an algorithm is provided to construct equivalence maps among such networks.     

一种高阶混合互连网络拓扑结构

随着对高性能计算机性能需求的不断提升,高性能计算机的系统规模在逐渐扩大,系统内的互连网络已经成为影响性能的关键因素。如何基于高阶路由器构建更大规模、更低网络延迟以及成本、更高网络吞吐率的互连网络,是目前的主要研究方向。针对目前广泛应用的高阶网络进行特性分析,并对其中的环网以及树网进行综合,提出了一种新型层次化混合互连网络拓扑结构。该结构具有良好的可扩展性以及通信能力,并在网络模拟器NetSim上对其性能进行了仿真和分析。     

Adaptive flow control in high-performance interconnection networks

The flow-control mechanism determinates the manner in which the communicational resources are allocated. Well-designed flow-control mechanism should provide efficient allocation of the communicational resources in wide variety of interconnection networks. The goal of this paper is to suggest a highly effective “Step-Back-on-Blocking” buffered flow control. The proposed flow-control mechanism combines the advantages of the Wormhole and Virtual-Cut Through flow controls, whilst adds a means for adaptive allocation of the communicational resources. The “Step-Back-on-Blocking” flow control provides low message latency and achieves high fraction of the channel bandwidth by performing conditional evasion of temporary blocked network resources. The effectiveness of the proposed flow control has been evaluated on the basis of numerous experiments conducted in OMNet++ discrete event simulation environment.     

SLA-controlled interconnection charging in next generation networks

Next generation network (NGN) should facilitate a single party to establish quality of service (QoS) enabled path between the two IP providers mutually interconnected by one or more transit providers. For that purpose, an end-to-end service level agreement (SLA) should be negotiated and maintained. In this article, we propose interconnection charging, which is controlled by the end-to-end SLA. Relationships between the required, offered, and actually achieved inter-provider QoS are quantified through the degrees of offering and provisioning, at both end-to-end and per-domain levels. Nominal retail price offered to end users and interconnection costs related with particular SLA are then corrected if needed, depending on the offered and provisioned QoS levels. We further propose five policies for interconnection charging and compare them under different QoS provisioning scenarios. Results of the analysis indicate that a properly selected SLA-controlled interconnection charging policy should encourage providers: (1) to offer services with different QoS levels; (2) to offer service that perfectly or most approximately matches the required QoS and (3) to achieve the contracted QoS level.     

Analytic models for multistage interconnection networks

Central to all parallel architectures is a switching network which facilitates the communication between a machine's components necessary to support their cooperation. Multistage interconnection networks (MINs) are classified and analytic models are described for both packet-switched and circuit-switched MINs with asynchronous transmission mode. Under strong enough assumptions, packet switching can be modeled by standard queuing methods, hence providing a standard against which to assess approximate models. We describe one such approximate model with much weaker assumptions which is more widely applicable and can be implemented more efficiently. To model circuit switching requires a different approach because of the presence of passive resources, namely multiple links through the MIN which must be held before a message can be transmitted and throughout its transmission. An approximate analysis based upon the recursive structure of a particular MIN topology which yields accurate predictions when compared with simulation is described.     

The cross product of interconnection networks

We study the cross product as a method for generating and analyzing interconnection network topologies for multiprocessor systems. Consider two interconnection graphs G₁ and G₂ each with some established properties such as symmetry, low degree and diameter, scalability, simple optimal routing, recursive structure (partitionability), fault tolerance, existence of node-disjoint paths, low cost embedding, and efficient broadcasting. We investigate and evaluate the corresponding properties for the cross product of G₁ and G₂ based on the properties of G₁ and those of G₂. We also give a mathematical characterization of product families of graphs which are closed under the cross product operation. This investigation is useful in two ways. On one hand, it gives a new tool for further studying some of the known interconnection topologies, such as the hypercube and the mesh, which can be defined using the cross product operation. On the other hand, it can be used in defining and evaluating new interconnection graphs using the cross product operation on known topologies     

Reducing accidental complexity in domain models

A fundamental principle in engineering, including software engineering, is to minimize the amount of accidental complexity which is introduced into engineering solutions due to mismatches between a problem and the technology used to represent the problem. As model-driven development moves to the center stage of software engineering, it is particularly important that this principle be applied to the technologies used to create and manipulate models, especially models that are intended to be free of solution decisions. At present, however, there is a significant mismatch between the “two level” modeling paradigm used to construct mainstream domain models and the conceptual information such models are required to represent—a mismatch that makes such models more complex than they need be. In this paper, we identify the precise nature of the mismatch, discuss a number of more or less satisfactory workarounds, and show how it can be avoided.     

Minimum feedback vertex sets in shuffle-based interconnection networks

Given a graph G, the problem is to construct a smallest subset S of vertices whose deletion results in an acyclic subgraph. The set S is called a minimum feedback vertex set for G.Tight upper and lower bounds on the cardinality of minimum feedback vertex sets have been previously obtained for some hypercube-like networks, such as meshes, tori, butterflies, cube-connected cycles and hypercubes. In this paper we construct minimum feedback vertex sets and determine their cardinalities in certain shuffle-based interconnection networks, such as shuffle-exchange, de Bruijn and Kautz networks.     

Characterization of spatial fault patterns in interconnection networks

Parallel computers, such as multiprocessors system-on-chip (Mp-SoCs), multicomputers and cluster computers, are consisting of hundreds or thousands multiple processing units and components (such as routers, channels and connectors) connected via some interconnection network that collectively may undergo high failure rates. Therefore, these systems are required to be equipped with fault-tolerant mechanisms to ensure that the system will keep running in a degraded mode. Normally, the faulty components are coalesced into fault regions, which are classified into two major categories: convex and concave regions. In this paper, we propose the first solution to calculate the probability of occurrences of common fault patterns in torus and mesh interconnection networks which includes both convex (-shaped, □-shaped) and concave (L-shaped, T-shaped, +-shaped, H-shaped) regions. These results play a key role when studying, particularly, the performance analysis of routing algorithms proposed for interconnection networks under faulty conditions.     

The load balancing problem in OTIS-Hypercube interconnection networks

An interconnection network architecture that promises to be an interesting option for future-generation parallel processing systems is the OTIS (Optical Transpose Interconnection System) optoelectronic architecture. Therefore, all performance improvement aspects of such a promising architecture need to be investigated; one of which is load balancing technique. This paper focuses on devising an efficient algorithm for load balancing on the promising OTIS-Hypercube interconnection networks. The proposed algorithm is called Clusters Dimension Exchange Method (CDEM). The analytical model and the experimental evaluation proved the excellence of OTIS-Hypercube compared to Hypercube in terms of various parameters, including execution time, load balancing accuracy, number of communication steps, and speed.

Stability measures of some static interconnection networks

It is important that a communication service has to service dependability by high level. Many affairs cause failures in a network. Destroying nodes or links in communication network, cable cuts, node interruptions, software errors or hardware failures and transmission failure at various points, human error or accident and can interrupt service for long periods of time. At the beginning a communication network, requiring greater degree of stability or less vulnerability. In this work, various stability measures of a communication network are defined and the stability measures of some static interconnection networks which are known long times and w-star networks that are a new graph class, are given.     

Study of General Icomplete Star Interconnection Networks

The star networks,which were originally proposed by Akers and Harel,have suffered from a rigorous restriction on the number of nodes.The general incomplete star networks(GISN) are proposed in this paper to relieve this restriction.An efficient labeling scheme for GISN is given,and routing and broadcasting algorithms are also presented for GIS.The communication diameter of GISN is shown to be bounded by 4n-7.The proposed single node broadcasting algorithm is optimal with respect to time complexity O(nlog2n).     

Adaptive routing protocols for hypercube interconnection networks

A taxonomy for characterizing adaptive routing protocols for hypercube interconnection networks (HINs) is presented. The taxonomy is based on classes of routing decisions common to any HIN. This taxonomy is used to discuss existing and proposed protocols. Rather than an exhaustive enumeration of related research, the protocols selected for discussion are intended to be representative of the classes defined by the taxonomy. These protocols are candidates for use in massively parallel architectures configured with HINs. To provide some insight into their behavior in very large HINs, results of simulation studies of representative protocols are presented