Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

Voronoi diagrams—a survey of a fundamental geometric data structure

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

We survey the current techniques to cope with the problem of string matching that allows errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices. We conclude with some directions for future work and open problems.

/pdf/a-guided-tour-to-approximate-string-matching-22fowlmq5b.pdf

A guided tour to approximate string matching

This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.

Algorithms in Combinatorial Geometry

Formal Concept Analysis

The paper considers the exact number of character comparisons needed to find all occurrences of a pattern of length m in a text of length n using on-line and general algorithms. For on-line algorithms, a lower bound of about (1 + &) . n character comparisons is obtained. For general algorithms, a lower bound of about (1 + &) . n character comparisons is obtained. These lower bounds complement an on-line upper bound of about (1 ,+ &)) n comparisons obtained recently by Cole and Hariharan. The lower bounds are obtained by finding pattems with interesting combinatorial properties (these are the hard to find patterns). It is also shown that for some patterns off-line algorithms can be more efficient than on-line algorithms.

Which patterns are hard to find

The unprecedented growth of the Internet over the past decade and of data collection, more generally, has given rise to vast quantities of digital information, ranging from web documents and images, genomic databases to a vast array of business customer information. Consequently, it is of growing importance to develop tools and models that enable us to better understand this data and to design data-driven algorithms that leverage this information. This thesis provides several fundamental theoretical and algorithmic results for tackling such problems with applications to speech recognition, image processing, natural language processing, computational biology and web-based algorithms. (1) Probabilistic automata provide an efficient and compact way to model sequence-oriented data such as speech or web documents. Measuring the similarity of such automata provides a way of comparing the objects they model, and is an essential first step in organizing this type of data. We present algorithmic and hardness results for computing various discrepancies (or dissimilarities) between probabilistic automata, including the relative entropy and the Lp distance; we also give an efficient algorithm to determine if two probabilistic automata are equivalent. In addition, we study the complexity of computing the norms of probabilistic automata. (2) Widespread success of search engines and information retrieval systems has led to large scale collection of rating information which is being used to provide personalized rankings. We examine an alternate formulation of the ranking problem for search engines motivated by the requirement that in addition to accurately predicting pairwise ordering, ranking systems must also preserve the magnitude of the preferences or the difference between ratings. We present algorithms with sound theoretical properties, and verify their efficacy through experiments. (3) Organizing and querying large amounts of digitized data such as images and videos is a challenging task because little or no label information is available. This motivates transduction, a setting in which the learning algorithm can leverage unlabeled data during training to improve performance. We present novel error bounds for a family of transductive regression algorithms and validate their usefulness through experiments. (4) Finally, price discovery in a market setting can be viewed as an (ongoing) learning problem. Specifically, the problem is to find and maintain a set of prices that balance supply and demand, a core topic in economics. This appears to involve complex implicit and possibly large-scale information transfers. We show that finding equilibrium prices, even approximately, in discrete markets is NP-hard and complement the hardness result with a matching polynomial time approximation algorithm. We also give a new way of measuring the quality of an approximation to equilibrium prices that is based on a natural aggregation of the dissatisfaction of individual market participants.

/pdf/theory-and-algorithms-for-modern-problems-in-machine-hfl8j013wm.pdf

Theory and algorithms for modern problems in machine learning and an analysis of markets

A major goal in Algorithmic Game Theory is to justify equilibrium concepts from an algorithmic and complexity perspective. One appealing approach is to identify robust natural distributed algorithms that converge quickly to an equilibrium. This paper addresses a lack of robustness in existing convergence results for discrete forms of tatonnement, including the fact that it need not converge when buyers have linear utility functions. This work achieves greater robustness by seeking approximate rather than exact convergence in large market settings. 
More specifically, this paper shows that for Fisher markets with buyers having CES utility functions, including linear utility functions, tatonnement will converge quickly to an approximate equilibrium (i.e. at a linear rate), modulo a suitable large market assumption. The quality of the approximation is a function of the parameters of the large market assumption.

Balancing the Robustness and Convergence of Tatonnement

Gradient descent, and coordinate descent in particular, are core tools in machine learning and elsewhere. Large problem instances are common. To help solve them, two orthogonal approaches are known: acceleration and parallelism. In this work, we ask whether they can be used simultaneously. The answer is "yes". 
More specifically, we consider an asynchronous parallel version of the accelerated coordinate descent algorithm proposed and analyzed by Lin, Liu and Xiao (SIOPT'15). We give an analysis based on the efficient implementation of this algorithm. The only constraint is a standard bounded asynchrony assumption, namely that each update can overlap with at most q others. (q is at most the number of processors times the ratio in the lengths of the longest and shortest updates.) We obtain the following three results: 
1. A linear speedup for strongly convex functions so long as q is not too large. 
2. A substantial, albeit sublinear, speedup for strongly convex functions for larger q. 
3. A substantial, albeit sublinear, speedup for convex functions.

An Analysis of Asynchronous Stochastic Accelerated Coordinate Descent.

Formal concept analysis (FCA) is a technique for knowledge visualisation. Several software tools have been developed to aid knowledge exploration using FCA, the most prevelant of these being TOSCANA. This paper describes a tool to allow the creation of conceptual scales by a domain expert. The tool employs techniques of direct manipulation to provide the user with an intuitive understanding of FCA. Examples from a case study employing Medical Subject Headings (MeSH) and a set of medical texts.

Richard Cole

Papers

Which patterns are hard to find

Theory and algorithms for modern problems in machine learning and an analysis of markets

Balancing the Robustness and Convergence of Tatonnement

An Analysis of Asynchronous Stochastic Accelerated Coordinate Descent.

Constructing conceptual scales in formal concept analysis