Richard Cole

Bio: Richard Cole is an academic researcher from New York University. The author has contributed to research in topics: Parallel algorithm & Time complexity. The author has an hindex of 57, co-authored 193 publications receiving 10474 citations. Previous affiliations of Richard Cole include Courant Institute of Mathematical Sciences & Tel Aviv University.

Optimal parallel algorithms for point-set and polygon problems

Abstract: In this paper we give parallel algorithms for a number of problems defined on point sets and polygons. All our algorithms have optimalT(n) * P(n) products, whereT(n) is the time complexity andP(n) is the number of processors used, and are for the EREW PRAM or CREW PRAM models. Our algorithms provide parallel analogues to well-known phenomena from sequential computational geometry, such as the fact that problems for polygons can oftentimes be solved more efficiently than point-set problems, and that nearest-neighbor problems can be solved without explicitly constructing a Voronoi diagram.

Geometric applications of Davenport-Schinzel sequences

Abstract: We present efficient algorithms for the following geometric problems: (i) Preprocessing of a 2-D polyhedral terrain so as to support fast ray shooting queries from a fixed point. (ii) Determining whether two disjoint interlocking simple polygons can be separated from one another by a sequence of translations. (iii) Determining whether a given convex polygon can be translated and rotated so as to fit into another given polygonal region. (iv) Motion planning for a convex polygon in the plane amidst polygonal barriers. All our algorithms make use of Davenport Schinzel sequences and on some generalizations of them; these sequences are a powerful combinatorial tool applicable in contexts which involve the calculation of the pointwise maximum or minimum of a collection of functions.

A fast algorithm for computing steiner edge connectivity

Abstract: Given an undirected graph or an Eulerian directed graph G and a subset S of its vertices, we show how to determine the edge connectivity C of the vertices in S in time O(C3 n log n+m). This algorithm is based on an efficient construction of tree packings which generalizes Edmonds' Theorem. These packings also yield a characterization of all minimal Steiner cuts of size C from which an efficient data structure for maintaining edge connectivity between vertices in S under edge insertion can be obtained. This data structure enables the efficient construction of a cactus tree for representing significant C-cuts among these vertices, called C-separations, in the same time bound. In turn, we use the cactus tree to give a fast implementation of an approximation algorithm for the Survivable Network Design problem due to Williamson, Goemans, Mihail and Vazirani.

Geometric retrieval problems

Abstract: A large class of geometric retrieval problems has the following form. Given a set X of geometric objects, preprocess to obtain a data structure D(X). Now use D(X) to rapidly answer queries on X. We say an algorithm for such a problem has (worst-case) space-time complexity O(f(n),g(n)) if the space requirement for D(X) is O(f) and the 'locate run-time' required for each retrieval is O(g). We show three techniques which can consistently be exploited in solving such problems. For instance, using our techniques, we obtain an O(n2+e, lognlog(l/∈)) spacetime algorithm for the polygon retrieval problem, for arbitrarily small ∈, improving on the previous solution having complexity O(n7,logn).

Tatonnement in ongoing markets of complementary goods

Abstract: This paper continues the study, initiated by Cole and Fleischer in [Cole and Fleischer 2008], of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak gross substitutes property and had bounded demand and income elasticities.The current work shows that fast convergence also occurs for the following type of markets: All pairs of goods are complements to each other, and the demand and income elasticities are suitably bounded.In particular, these conditions hold when all buyers in the market are equipped with CES utilities, where all the parameters ρ, one per buyer, satisfy -1

Voronoi diagrams—a survey of a fundamental geometric data structure

Abstract: 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

Principles and Practices of Interconnection Networks

Abstract: 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

A guided tour to approximate string matching

Abstract: 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.

Algorithms in Combinatorial Geometry

Abstract: 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.