This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the ``LINE,'' which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online\footnote{\url{https://github.com/tangjianpku/LINE}}.

/pdf/line-large-scale-information-network-embedding-nelm7n6nct.pdf

LINE: Large-scale Information Network Embedding

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.

One of the greatest challenges faced by designers of digital systems is optimizing the communication and interconnection between system components. Interconnection networks offer an attractive and economical solution to this communication crisis and are fast becoming pervasive in digital systems. Current trends suggest that this communication bottleneck will be even more problematic when designing future generations of machines. Consequently, the anatomy of an interconnection network router and science of interconnection network design will only grow in importance in the coming years.

This book offers a detailed and comprehensive presentation of the basic principles of interconnection network design, clearly illustrating them with numerous examples, chapter exercises, and case studies. It incorporates hardware-level descriptions of concepts, allowing a designer to see all the steps of the process from abstract design to concrete implementation.

·Case studies throughout the book draw on extensive author experience in designing interconnection networks over a period of more than twenty years, providing real world examples of what works, and what doesn't.

·Tightly couples concepts with implementation costs to facilitate a deeper understanding of the tradeoffs in the design of a practical network.

·A set of examples and exercises in every chapter help the reader to fully understand all the implications of every design decision.

Table of Contents


Chapter 1 Introduction to Interconnection Networks 
1.1 Three Questions About Interconnection Networks 
1.2 Uses of Interconnection Networks 
1.3 Network Basics 
1.4 History 
1.5 Organization of this Book 

Chapter 2 A Simple Interconnection Network 
2.1 Network Specifications and Constraints 
2.2 Topology 
2.3 Routing 
2.4 Flow Control 
2.5 Router Design 
2.6 Performance Analysis 
2.7 Exercises 

Chapter 3 Topology Basics 
3.1 Nomenclature 
3.2 Traffic Patterns 
3.3 Performance 
3.4 Packaging Cost 
3.5 Case Study: The SGI Origin 2000 
3.6 Bibliographic Notes 
3.7 Exercises 

Chapter 4 Butterfly Networks 
4.1 The Structure of Butterfly Networks 
4.2 Isomorphic Butterflies 
4.3 Performance and Packaging Cost 
4.4 Path Diversity and Extra Stages 
4.5 Case Study: The BBN Butterfly 
4.6 Bibliographic Notes 
4.7 Exercises 

Chapter 5 Torus Networks 
5.1 The Structure of Torus Networks 
5.2 Performance 
5.3 Building Mesh and Torus Networks 
5.4 Express Cubes 
5.5 Case Study: The MIT J-Machine 
5.6 Bibliographic Notes 
5.7 Exercises 
Chapter 6 Non-Blocking Networks 
6.1 Non-Blocking vs. Non-Interfering Networks 
6.2 Crossbar Networks 
6.3 Clos Networks 
6.4 Benes Networks 
6.5 Sorting Networks 
6.6 Case Study: The Velio VC2002 (Zeus) Grooming Switch 
6.7 Bibliographic Notes 
6.8 Exercises 

Chapter 7 Slicing and Dicing 
7.1 Concentrators and Distributors 
7.2 Slicing and Dicing 
7.3 Slicing Multistage Networks 
7.4 Case Study: Bit Slicing in the Tiny Tera 
7.5 Bibliographic Notes 
7.6 Exercises 

Chapter 8 Routing Basics 
8.1 A Routing Example 
8.2 Taxonomy of Routing Algorithms 
8.3 The Routing Relation 
8.4 Deterministic Routing 
8.5 Case Study: Dimension-Order Routing in the Cray T3D 
8.6 Bibliographic Notes 
8.7 Exercises 

Chapter 9 Oblivious Routing 
9.1 Valiant's Randomized Routing Algorithm 
9.2 Minimal Oblivious Routing 
9.3 Load-Balanced Oblivious Routing 
9.4 Analysis of Oblivious Routing 
9.5 Case Study: Oblivious Routing in the
Avici Terabit Switch Router(TSR) 
9.6 Bibliographic Notes 
9.7 Exercises 

Chapter 10 Adaptive Routing 
10.1 Adaptive Routing Basics 
10.2 Minimal Adaptive Routing 
10.3 Fully Adaptive Routing 
10.4 Load-Balanced Adaptive Routing 
10.5 Search-Based Routing 
10.6 Case Study: Adaptive Routing in the
Thinking Machines CM-5 
10.7 Bibliographic Notes 
10.8 Exercises 

Chapter 11 Routing Mechanics 
11.1 Table-Based Routing 
11.2 Algorithmic Routing 
11.3 Case Study: Oblivious Source Routing in the
IBM Vulcan Network 
11.4 Bibliographic Notes 
11.5 Exercises 

Chapter 12 Flow Control Basics 
12.1 Resources and Allocation Units 
12.2 Bufferless Flow Control 
12.3 Circuit Switching 
12.4 Bibliographic Notes 
12.5 Exercises 

Chapter 13 Buffered Flow Control 
13.1 Packet-Buffer Flow Control 
13.2 Flit-Buffer Flow Control 
13.3 Buffer Management and Backpressure 
13.4 Flit-Reservation Flow Control 
13.5 Bibliographic Notes 
13.6 Exercises 

Chapter 14 Deadlock and Livelock 
14.1 Deadlock 
14.2 Deadlock Avoidance 
14.3 Adaptive Routing 
14.4 Deadlock Recovery 
14.5 Livelock 
14.6 Case Study: Deadlock Avoidance in the Cray T3E 
14.7 Bibliographic Notes 
14.8 Exercises 

Chapter 15 Quality of Service 
15.1 Service Classes and Service Contracts 
15.2 Burstiness and Network Delays 
15.3 Implementation of Guaranteed Services 
15.4 Implementation of Best-Effort Services 
15.5 Separation of Resources 
15.6 Case Study: ATM Service Classes 
15.7 Case Study: Virtual Networks in the Avici TSR 
15.8 Bibliographic Notes 
15.9 Exercises 

Chapter 16 Router Architecture 
16.1 Basic Router Architecture 
16.2 Stalls 
16.3 Closing the Loop with Credits 
16.4 Reallocating a Channel 
16.5 Speculation and Lookahead 
16.6 Flit and Credit Encoding 
16.7 Case Study: The Alpha 21364 Router 
16.8 Bibliographic Notes 
16.9 Exercises 

Chapter 17 Router Datapath Components 
17.1 Input Buffer Organization 
17.2 Switches 
17.3 Output Organization 
17.4 Case Study: The Datapath of the IBM Colony
Router 
17.5 Bibliographic Notes 
17.6 Exercises 

Chapter 18 Arbitration 
18.1 Arbitration Timing 
18.2 Fairness 
18.3 Fixed Priority Arbiter 
18.4 Variable Priority Iterative Arbiters 
18.5 Matrix Arbiter 
18.6 Queuing Arbiter 
18.7 Exercises 

Chapter 19 Allocation 
19.1 Representations
19.2 Exact Algorithms
19.3 Separable Allocators 
19.4 Wavefront Allocator 
19.5 Incremental vs. Batch Allocation 
19.6 Multistage Allocation 
19.7 Performance of Allocators 
19.8 Case Study: The Tiny Tera Allocator 
19.9 Bibliographic Notes 
19.10 Exercises

Chapter 20 Network Interfaces 
20.1 Processor-Network Interface 
20.2 Shared-Memory Interface 
20.3 Line-Fabric Interface 
20.4 Case Study: The MIT M-Machine Network Interface 
20.5 Bibliographic Notes 
20.6 Exercises 

Chapter 21 Error Control 411
21.1 Know Thy Enemy: Failure Modes and Fault Models 
21.2 The Error Control Process: Detection, Containment,
and Recovery 
21.3 Link Level Error Control 
21.4 Router Error Control 
21.5 Network-Level Error Control 
21.6 End-to-end Error Control 
21.7 Bibliographic Notes 
21.8 Exercises 

Chapter 22 Buses 
22.1 Bus Basics 
22.2 Bus Arbitration 
22.3 High Performance Bus Protocol 
22.4 From Buses to Networks 
22.5 Case Study: The PCI Bus 
22.6 Bibliographic Notes 
22.7 Exercises 

Chapter 23 Performance Analysis 
23.1 Measures of Interconnection Network Performance 
23.2 Analysis 
23.3 Validation
23.4 Case Study: Efficiency and Loss in the
BBN Monarch Network 
23.5 Bibliographic Notes 
23.6 Exercises 

Chapter 24 Simulation 
24.1 Levels of Detail 
24.2 Network Workloads 
24.3 Simulation Measurements 
24.4 Simulator Design 
24.5 Bibliographic Notes 
24.6 Exercises 

Chapter 25 Simulation Examples 495
25.1 Routing
25.2 Flow Control Performance 
25.3 Fault Tolerance 

Appendix A Nomenclature 
Appendix B Glossary 
Appendix C Network Simulator

Principles and Practices of Interconnection Networks

A main distinguishing feature of a wireless network compared with a wired network is its broadcast nature, in which the signal transmitted by a node may reach several other nodes, and a node may receive signals from several other nodes simultaneously. Rather than a blessing, this feature is treated more as an interference-inducing nuisance in most wireless networks today (e.g., IEEE 802.11). The goal of this paper is to show how the concept of network coding can be applied at the physical layer to turn the broadcast property into a capacity-boosting advantage in wireless ad hoc networks. Specifically, we propose a physical-layer network coding (PNC) scheme to coordinate transmissions among nodes. In contrast to "straightforward" network coding which performs coding arithmetic on digital bit streams after they have been received, PNC makes use of the additive nature of simultaneously arriving electromagnetic (EM) waves for equivalent coding operation. PNC can yield higher capacity than straight-forward network coding when applied to wireless networks. We believe this is a first paper that ventures into EM-wave-based network coding at the physical layer and demonstrates its potential for boosting network capacity. PNC opens up a whole new research area because of its implications and new design requirements for the physical, MAC, and network layers of ad hoc wireless stations. The resolution of the many outstanding but interesting issues in PNC may lead to a revolutionary new paradigm for wireless ad hoc networking.

Hot topic: physical-layer network coding

There is mounting concern that social media sites contribute to political polarization by creating “echo chambers” that insulate people from opposing views about current events. We surveyed a large sample of Democrats and Republicans who visit Twitter at least three times each week about a range of social policy issues. One week later, we randomly assigned respondents to a treatment condition in which they were offered financial incentives to follow a Twitter bot for 1 month that exposed them to messages from those with opposing political ideologies (e.g., elected officials, opinion leaders, media organizations, and nonprofit groups). Respondents were resurveyed at the end of the month to measure the effect of this treatment, and at regular intervals throughout the study period to monitor treatment compliance. We find that Republicans who followed a liberal Twitter bot became substantially more conservative posttreatment. Democrats exhibited slight increases in liberal attitudes after following a conservative Twitter bot, although these effects are not statistically significant. Notwithstanding important limitations of our study, these findings have significant implications for the interdisciplinary literature on political polarization and the emerging field of computational social science.

Exposure to opposing views on social media can increase political polarization

The process of categorizing packets into "flows" in an Internet router is called packet classification. All packets belonging to the same flow obey a predefined rule and are processed in a similar manner by the router. For example, all packets with the same source and destination IP addresses may be defined to form a flow. Packet classification is needed for non-best-effort services, such as firewalls and quality of service; services that require the capability to distinguish and isolate traffic in different flows for suitable processing. In general, packet classification on multiple fields is a difficult problem. Hence, researchers have proposed a variety of algorithms which, broadly speaking, can be categorized as basic search algorithms, geometric algorithms, heuristic algorithms, or hardware-specific search algorithms. In this tutorial we describe algorithms that are representative of each category, and discuss which type of algorithm might be suitable for different applications.

/pdf/algorithms-for-packet-classification-47paaaxzc2.pdf

Algorithms for packet classification

Routers classify packets to determine which flow they belong to, and to decide what service they should receive. Classification may, in general, be based on an arbitrary number of fields in the packet header. Performing classification quickly on an arbitrary number of fields is known to be difficult, and has poor worst-case performance. In this paper, we consider a number of classifiers taken from real networks. We find that the classifiers contain considerable structure and redundancy that can be exploited by the classification algorithm. In particular, we find that a simple multi-stage classification algorithm, called RFC (recursive flow classification), can classify 30 million packets per second in pipelined hardware, or one million packets per second in software.

/pdf/packet-classification-on-multiple-fields-2f4q88xpwm.pdf

Packet classification on multiple fields

The increased bandwidth in the Internet puts great demands on network routers; for example, to route minimum sized Gigabit Ethernet packets, an IP router must process about 1.5/spl times/10/sup 6/ packets per second per port. Using the "rule-of-thumb" that it takes roughly 1000 packets per second for every 10/sup 6/ bits per second of line rate, an OC-192 line requires 10/spl times/10/sup 6/ routing lookups per second; well above current router capabilities. One limitation of router performance is the route lookup mechanism. IP routing requires that a router perform a longest-prefix-match address lookup for each incoming datagram in order to determine the datagram's next hop. We present a route lookup mechanism that when implemented in a pipelined fashion in hardware, can achieve one route lookup every memory access. With current 50 ns DRAM, this corresponds to approximately 20/spl times/10/sup 6/ packets per second; much faster than current commercially available routing lookup schemes. We also present novel schemes for performing quick updates to the forwarding table in hardware. We demonstrate using real routing update patterns that the routing tables can be updated with negligible overhead to the central processor.

/pdf/routing-lookups-in-hardware-at-memory-access-speeds-1xpkmtqlt5.pdf

Routing lookups in hardware at memory access speeds

WTF ("Who to Follow") is Twitter's user recommendation service, which is responsible for creating millions of connections daily between users based on shared interests, common connections, and other related factors. This paper provides an architectural overview and shares lessons we learned in building and running the service over the past few years. Particularly noteworthy was our design decision to process the entire Twitter graph in memory on a single server, which significantly reduced architectural complexity and allowed us to develop and deploy the service in only a few months. At the core of our architecture is Cassovary, an open-source in-memory graph processing engine we built from scratch for WTF. Besides powering Twitter's user recommendations, Cassovary is also used for search, discovery, promoted products, and other services as well. We describe and evaluate a few graph recommendation algorithms implemented in Cassovary, including a novel approach based on a combination of random walks and SALSA. Looking into the future, we revisit the design of our architecture and comment on its limitations, which are presently being addressed in a second-generation system under development.

/pdf/wtf-the-who-to-follow-service-at-twitter-3j1yvrx2d4.pdf

WTF: the who to follow service at Twitter

Increasing demands on Internet router performance and functionality create a need for algorithms that classify packets quickly with minimal storage requirements and allow frequent updates. Unlike previous algorithms, the algorithm proposed here meets this need well by using heuristics that exploit structure present in classifiers. Our approach, which we call HiCuts (hierarchical intelligent cuttings), attempts to partition the search space in each dimension, guided by simple heuristics that exploit the classifier's structure. We discover this structure by preprocessing the classifier. We can tune the algorithm's parameters to trade off query time against storage requirements. In classifying packets based on four header fields, HiCuts performs quickly and requires relatively little storage compared with previously described algorithms.

Classifying packets with hierarchical intelligent cuttings

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