External Memory Algorithms

Describes several useful paradigms for the design and implementation of efficient external memory (EM) algorithms and data structures. The problem domains considered include sorting, permuting, FFT, scientific computing, computational geometry, graphs, databases, geographic information systems, and text and string processing.

The algorithms involve using techniques from computer science and mathematics to solve combinatorial problems whose associated data require the use of a hierarchy of storage devices. The 15 papers discuss such topics as synopsis data structures for massive data sets, maximum clique problems in very large graphs, concrete software libraries, computing on data streams, efficient cross-trees for external memory, efficient schemes for distributing data on parallel memory systems, and external memory techniques for iso-surface extraction in scientific visualization. Annotation copyrighted by Book News, Inc., Portland, OR.

Algorithms that have to process large data sets have to take into account that the cost of memory access depends on where the data is stored. Traditional algorithm design is based on the von Neumann model where accesses to memory have uniform cost. Actual machines increasingly deviate from this model: while waiting for memory access, nowadays, microprocessors can in principle execute 1000 additions of registers; for hard disk access this factor can reach six orders of magnitude. The 16 coherent chapters in this monograph-like tutorial book introduce and survey algorithmic techniques used to achieve high performance on memory hierarchies; emphasis is placed on methods interesting from a theoretical as well as important from a practical point of view.

Introduction -- Array-based lists -- Linked lists -- Skiplists -- Hash tables -- Binary trees -- Random binary search trees -- Scapegoat trees -- Red-black trees -- Heaps -- Sorting algorithms -- Graphs -- Data structures for integers -- External memory searching.

Massive modern datasets make traditional data structures and algorithms grind to a halt. This fun and practical guide introduces cutting-edge techniques that can reliably handle even the largest distributed datasets. In Algorithms and Data Structures for Massive Datasets you will learn: Probabilistic sketching data structures for practical problems Choosing the right database engine for your application Evaluating and designing efficient on-disk data structures and algorithms Understanding the algorithmic trade-offs involved in massive-scale systems Deriving basic statistics from streaming data Correctly sampling streaming data Computing percentiles with limited space resources Algorithms and Data Structures for Massive Datasets reveals a toolbox of new methods that are perfect for handling modern big data applications. You’ll explore the novel data structures and algorithms that underpin Google, Facebook, and other enterprise applications that work with truly massive amounts of data. These effective techniques can be applied to any discipline, from finance to text analysis. Graphics, illustrations, and hands-on industry examples make complex ideas practical to implement in your projects—and there’s no mathematical proofs to puzzle over. Work through this one-of-a-kind guide, and you’ll find the sweet spot of saving space without sacrificing your data’s accuracy. About the technology Standard algorithms and data structures may become slow—or fail altogether—when applied to large distributed datasets. Choosing algorithms designed for big data saves time, increases accuracy, and reduces processing cost. This unique book distills cutting-edge research papers into practical techniques for sketching, streaming, and organizing massive datasets on-disk and in the cloud. About the book Algorithms and Data Structures for Massive Datasets introduces processing and analytics techniques for large distributed data. Packed with industry stories and entertaining illustrations, this friendly guide makes even complex concepts easy to understand. You’ll explore real-world examples as you learn to map powerful algorithms like Bloom filters, Count-min sketch, HyperLogLog, and LSM-trees to your own use cases. What's inside Probabilistic sketching data structures Choosing the right database engine Designing efficient on-disk data structures and algorithms Algorithmic tradeoffs in massive-scale systems Computing percentiles with limited space resources About the reader Examples in Python, R, and pseudocode. About the author Dzejla Medjedovic earned her PhD in the Applied Algorithms Lab at Stony Brook University, New York. Emin Tahirovic earned his PhD in biostatistics from University of Pennsylvania. Illustrator Ines Dedovic earned her PhD at the Institute for Imaging and Computer Vision at RWTH Aachen University, Germany. Table of Contents 1 Introduction PART 1 HASH-BASED SKETCHES 2 Review of hash tables and modern hashing 3 Approximate membership: Bloom and quotient filters 4 Frequency estimation and count-min sketch 5 Cardinality estimation and HyperLogLog PART 2 REAL-TIME ANALYTICS 6 Streaming data: Bringing everything together 7 Sampling from data streams 8 Approximate quantiles on data streams PART 3 DATA STRUCTURES FOR DATABASES AND EXTERNAL MEMORY ALGORITHMS 9 Introducing the external memory model 10 Data structures for databases: B-trees, Bε-trees, and LSM-trees 11 External memory sorting

Nowadays, textual databases are among the most rapidly growing collections of data. Some of these collections contain a new type of data that differs from classical numerical or textual data. These are long sequences of symbols, not divided into well-separated small tokens (words). The most prominent among such collections are databases of biological sequences, which are experiencing today an unprecedented growth rate. Starting in 2008, the "1000 Genomes Project" has been launched with the ultimate goal of collecting sequences of additional 1,500 Human genomes, 500 each of European, African, and East Asian origin. This will produce an extensive catalog of Human genetic variations. The size of just the raw sequences in this catalog would be about 5 terabytes. Querying strings without well-separated tokens poses a different set of challenges, typically addressed by building full-text indexes, which provide effective structures to index all the substrings of the given strings. Since full-text indexes occupy more space than the raw data, it is often necessary to use disk space for their construction. However, until recently, the construction of full-text indexes in secondary storage was considered impractical due to excessive I/O costs. Despite this, algorithms developed in the last decade demonstrated that efficient external construction of full-text indexes is indeed possible. This book is about large-scale construction and usage of full-text indexes. We focus mainly on suffix trees, and show efficient algorithms that can convert suffix trees to other kinds of full-text indexes and vice versa. There are four parts in this book. They are a mix of string searching theory with the reality of external memory constraints. The first part introduces general concepts of full-text indexes and shows the relationships between them. The second part presents the first series of external-memory construction algorithms that can handle the construction of full-text indexes for moderately large strings in the order of few gigabytes. The third part presents algorithms that scale for very large strings. The final part examines queries that can be facilitated by disk-resident full-text indexes. Table of Contents: Structures for Indexing Substrings / External Construction of Suffix Trees / Scaling Up: When the Input Exceeds the Main Memory / Queries for Disk-based Indexes / Conclusions and Open Problems