Abstract

AbstractThis chapter introduces the “sublinear computation paradigm.” A sublinear-time algorithm is an algorithm that runs in time sublinear in the size of the instance (input data). In other words, the running time iso(n), wherenis the size of the instance. This century marks the start of the era of big data. In order to manage big data, polynomial-time algorithms, which are considered to be efficient, may sometimes be inadequate because they may require too much time or computational resources. In such cases, sublinear-time algorithms are expected to work well. We call this idea the “sublinear computation paradigm.” A research project named “Foundations on Innovative Algorithms for Big Data (ABD),” in which this paradigm is the central concept, was started under the CREST program of the Japan Science and Technology Agency (JST) in October 2014 and concluded in September 2021. This book mainly introduces the results of this project.

Highlights

  • We Are in the Era of Big DataThe twenty-first century can be called the era of Big Data

  • This chapter introduces the “sublinear computation paradigm.” A sublineartime algorithm is an algorithm that runs in time sublinear in the size of the instance

  • If we assume that 106 bytes(≈ 107 bits) of data is contained in a single webpage on average,1 the total amount of the data stored on the Internet would be more than 100 exabits (=1020 bits)! The various actions that everyone performs are collected by our smartphones and are stored in the memory of storage devices around the world

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Summary

We Are in the Era of Big Data

The twenty-first century can be called the era of Big Data. The number of webpages on the Internet was estimated to be more than 1 trillion (=1012) in 2008 [22], and the number of websites grows ten times in these 10 years [21]. The number of webpages is estimated to be more than 10 trillion (=1013) now. If we assume that 106 bytes(≈ 107 bits) of data is contained in a single webpage on average, the total amount of the data stored on the Internet would be more than 100 exabits (=1020 bits)! The various actions that everyone performs are collected by our smartphones and are stored in the memory of storage devices around the world. The remarkable development of computer memory has made it possible to store this information

Ito (B)
Theory of Computational Complexity and Polynomial-Time Algorithms
A Brief History of Polynomial-Time Algorithms
Emergence of Sublinear-Time Algorithms
Property Testing and Parameter Testing
Ways to Decrease Computational Resources
Streaming Algorithms
Compression
Succinct Data Structures
Sublinear and Polynomial Computation Are Both Important
Research Project ABD

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