Author

# Richard Cole

Other affiliations: Courant Institute of Mathematical Sciences, Tel Aviv University, École Normale Supérieure

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

##### Papers published on a yearly basis

##### Papers

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TL;DR: A parallel implementation of merge sort on a CREW PRAM that uses n processors and O(logn) time; the constant in the running time is small.

Abstract: We give a parallel implementation of merge sort on a CREW PRAM that uses n processors and $O(\log n)$ time; the constant in the running time is small. We also give a more complex version of the algorithm for the EREW PRAM; it also uses n processors and $O(\log n)$ time. The constant in the running time is still moderate, though not as small.

821 citations

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22 Aug 2011

TL;DR: The algorithms apply a novel “random-like” deterministic technique that provides for a fast and efficient breaking of an apparently symmetric situation in parallel and distributed computation.

Abstract: The following problem is considered: given a linked list of length n , compute the distance from each element of the linked list to the end of the list. The problem has two standard deterministic algorithms: a linear time serial algorithm, and an O (log n ) time parallel algorithm using n processors. We present new deterministic parallel algorithms for the problem. Our strongest results are (1) O (log n log* n ) time using n /(log n log* n ) processors (this algorithm achieves optimal speed-up); (2) O (log n ) time using n log ( k ) n /log n processors, for any fixed positive integer k . The algorithms apply a novel “random-like” deterministic technique. This technique provides for a fast and efficient breaking of an apparently symmetric situation in parallel and distributed computation.

440 citations

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[...]

09 Sep 2011

TL;DR: In this paper, a parallel implementation of merge sort on a CREW PRAM that uses n processors and O(logn) time is given, and the constant in the running time is small.

Abstract: We give a parallel implementation of merge sort on a CREW PRAM that uses n processors and O(logn) time; the constant in the running time is small. We also give a more complex version of the algorithm for the EREW PRAM; it also uses n processors and O(logn) time. The constant in the running time is still moderate, though not as small.

345 citations

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13 Jun 2004

TL;DR: This paper considers various flavors of the following online problem: preprocess a text or collection of strings, so that given a query string p, all matches of p with the text can be reported quickly.

Abstract: This paper considers various flavors of the following online problem: preprocess a text or collection of strings, so that given a query string p, all matches of p with the text can be reported quickly. In this paper we consider matches in which a bounded number of mismatches are allowed, or in which a bounded number of "don't care" characters are allowed. The specific problems we look at are: indexing, in which there is a single text t, and we seek locations where p matches a substring of t; dictionary queries, in which a collection of strings is given upfront, and we seek those strings which match p in their entirety; and dictionary matching, in which a collection of strings is given upfront, and we seek those substrings of a (long) p which match an original string in its entirety. These are all instances of an all-to-all matching problem, for which we provide a single solution.The performance bounds all have a similar character. For example, for the indexing problem with n=|t| and m=|p|, the query time for k substitutions is O(m + (c1 log n)k⁄k! + # matches), with a data structure of size O(n (c2 log n)k⁄k!) and a preprocessing time of O(n (c2 log n)k⁄k!), where c1,c2 > 1 are constants. The deterministic preprocessing assumes a weakly nonuniform RAM model; this assumption is not needed if randomization is used in the preprocessing.

291 citations

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06 Sep 2015TL;DR: This paper provides a general method that trims a factor of O(log n) time for many applications of this technique.

Abstract: Megiddo introduced a technique for using a parallel algorithm for one problem to construct an efficient serial algorithm for a second problem. We give a general method that trims a factor o f 0(logn) time (or more) for many applications of this technique.

290 citations

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TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.

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

3,981 citations

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01 Jan 2004

TL;DR: 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, allowing a designer to see all the steps of the process from abstract design to concrete implementation.

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

3,149 citations

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TL;DR: This work surveys the current techniques to cope with the problem of string matching that allows errors, and focuses 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.

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.

2,515 citations

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01 Jan 1987TL;DR: This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems with an important role in this study.

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.

2,269 citations

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TL;DR: FCA explicitly formalises extension and intension of a concept, their mutual relationships, and the fact that increasing intent implies decreasing extent and vice versa, and allows to derive a concept hierarchy from a given dataset.

Abstract: Formal concept analysis (FCA) [71] is a mathematical theory for concepts and concept hierarchies that reflects an understanding of “concept” which is first mentioned explicitly in the Logic of Port Royal [2] in 1668 and has been established in the German standard ‘DIN 2330 – Concepts and terms; general principles’ [19]. FCA explicitly formalises extension and intension of a concept, their mutual relationships, and the fact that increasing intent implies decreasing extent and vice versa. Based on lattice theory, it allows to derive a concept hierarchy from a given dataset. FCA complements thus the usual ontology engineering approach, where the concept hierarchy is modeled manually. FCA differs from other knowledge representation formalisms (like RDF (see chapter “Resource Description Framework”), description logics (see chapter “Description Logics”), OWL (see chapter “Web Ontology Language: OWL”), or conceptual graphs [53]). The standard DIN 2330 [19] helps us pointing out the difference. It distinguishes three levels: object level, concept level, and representation level (see Fig. 1). There is no immediate relationship between objects and names. This relationship is rather provided by concepts. On the concept level, the objects under discussion constitute the extension of the concept, while their shared properties constitute the intension of the

1,957 citations