Sublinear Computation Paradigm: Algorithmic Revolution in the Big Data Era

403 Pages·2021·10.414 MB·English

by  Naoki Katoh (editor), Yuya Higashikawa (editor), Hiro Ito (editor), Atsuki Nagao (editor), Tetsuo Shibuya (editor), Adnan Sljoka (editor), Kazuyuki Tanaka (editor), Yushi Uno (editor)

Naoki Katoh · Yuya Higashikawa · Hiro Ito ·
Atsuki Nagao · Tetsuo Shibuya · Adnan Sljoka ·
Kazuyuki Tanaka · Yushi Uno   Editors
Sublinear
Computation
Paradigm
Algorithmic Revolution in the Big Data Era
Sublinear Computation Paradigm
Naoki Katoh Yuya Higashikawa
(cid:129) (cid:129)
Hiro Ito Atsuki Nagao
(cid:129) (cid:129)
Tetsuo Shibuya Adnan Sljoka
(cid:129) (cid:129)
Kazuyuki Tanaka Yushi Uno
(cid:129)
Editors
Sublinear Computation
Paradigm
Algorithmic Revolution in the Big Data Era
123
Editors
NaokiKatoh Yuya Higashikawa
Graduate Schoolof Information Science Graduate Schoolof Information Science
University of Hyogo University of Hyogo
Kobe,Hyogo,Japan Kobe,Hyogo,Japan
HiroIto Atsuki Nagao
Schoolof Informatics andEngineering Department ofInformation Science
University of Electro-Communications Ochanomizu University
Chofu, Tokyo,Japan Bunkyo,Tokyo,Japan
TetsuoShibuya Adnan Sljoka
Human GenomeCenter Centerfor AdvancedIntelligence Project
University of Tokyo RIKEN
Minato,Tokyo,Japan Chuo,Tokyo,Japan
Kazuyuki Tanaka YushiUno
Graduate Schoolof Information Science Graduate Schoolof Engineering
Tohoku University Osaka Prefecture University
Sendai, Miyagi,Japan Sakai, Osaka,Japan
ISBN978-981-16-4094-0 ISBN978-981-16-4095-7 (eBook)
https://doi.org/10.1007/978-981-16-4095-7
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Preface
This book gives an overview of cutting-edge work on a new paradigm called the
“sublinear computation paradigm,” which was proposed in the large multiyear
academicresearchproject“FoundationsofInnovativeAlgorithmsforBigData”in
Japan. In today's rapidly evolving age of big data, massive increases in big data
have led to many new opportunities and uncharted areas of exploration, but have
also brought new challenges. To handle the unprecedented explosion of big data
sets in research, industry, and other areas of society, there is an urgent need to
developnovelmethodsandapproachesforbigdataanalysis.Tomeetthisneed,we
are pursuing innovative changes in algorithm theory for big data. For example,
polynomial-time algorithms have thus far been regarded as “fast,” but if we apply
anOðn2Þ-timealgorithmtoapetabyte-scaleorlargerbigdataset,wewillencounter
problems in terms of computational resources or running time. To deal with this
critical computational and algorithmic bottleneck, we require linear, sublinear, and
constant-time algorithms. In this project, which ran from October 2014 to
September2021,wehaveproposedthesublinearcomputationparadigminorderto
supportinnovationinthebigdataera.Wehavecreatedafoundationofinnovative
algorithms bydeveloping computational procedures, data structures, and modeling
techniques for big data. The project is organized into three teams that focus on
sublinear algorithms, sublinear data structures, and sublinear modeling. Our work
has provided high-level academic research results of strong computational and
algorithmic interest, which are presented in this book.
This book consists of five parts: Part I, which consists of a single chapter
introducingtheconceptofthesublinearcomputationparadigm;PartsII,III,andIV
review results on sublinear algorithms, sublinear data structures, and sublinear
modeling, respectively; and Part V presents some application results.
v
vi Preface
We deeply appreciate the members of this project and everyone else who was
involved. This project was conducted as a subproject of the research project
“AdvancedCoreTechnologiesforBigDataIntegration,”whichwassupervisedby
Prof. Masaru Kitsuregawa. We would like to express our gratitude to him and
everyoneinvolvedinthatproject.WealsothanktheeditorialofficeofSpringerfor
the opportunity to publish this book.
Kobe, Japan Naoki Katoh
Tokyo, Japan Hiro Ito
Kobe, Japan Yuya Higashikawa
Contents
Part I Introduction
1 What Is the Sublinear Computation Paradigm? . . . . . . . . . . . . . . . 3
Naoki Katoh and Hiro Ito
Part II Sublinear Algorithms
2 Property Testing on Graphs and Games. . . . . . . . . . . . . . . . . . . . . 13
Hiro Ito
3 Constant-Time Algorithms for Continuous Optimization
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Yuichi Yoshida
4 Oracle-Based Primal-DualAlgorithms forPackingandCovering
Semidefinite Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Khaled Elbassioni and Kazuhisa Makino
5 Almost Linear Time Algorithms for Some Problems on Dynamic
Flow Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Yuya Higashikawa, Naoki Katoh, and Junichi Teruyama
Part III Sublinear Data Structures
6 Information Processing on Compressed Data . . . . . . . . . . . . . . . . . 89
Yoshimasa Takabatake, Tomohiro I, and Hiroshi Sakamoto
7 Compression and Pattern Matching . . . . . . . . . . . . . . . . . . . . . . . . 105
Takuya Kida and Isamu Furuya
8 Orthogonal Range Search Data Structures . . . . . . . . . . . . . . . . . . . 121
Kazuki Ishiyama and Kunihiko Sadakane
9 Enhanced RAM Simulation in Succinct Space . . . . . . . . . . . . . . . . 149
Taku Onodera
vii
viii Contents
Part IV Sublinear Modelling
10 Review of Sublinear Modeling in Probabilistic Graphical Models
by Statistical Mechanical Informatics and Statistical Machine
Learning Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Kazuyuki Tanaka
11 Empirical Bayes Method for Boltzmann Machines . . . . . . . . . . . . . 277
Muneki Yasuda
12 Dynamical Analysis of Quantum Annealing . . . . . . . . . . . . . . . . . . 295
Anthony C. C. Coolen, Theodore Nikoletopoulos, Shunta Arai,
and Kazuyuki Tanaka
13 Mean-Field Analysis of Sourlas Codes with Adiabatic
Reverse Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Shunta Arai
Part V Applications
14 Structural and Functional Analysis of Proteins
Using Rigidity Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Adnan Sljoka
15 Optimization of Evacuation and Walking-Home Routes
from Osaka City After a Nankai Megathrust Earthquake
Using Road Network Big Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
Atsushi Takizawa and Yutaka Kawagishi
16 Stream-Based Lossless Data Compression. . . . . . . . . . . . . . . . . . . . 391
Shinichi Yamagiwa
Part I
Introduction
Chapter 1
What Is the Sublinear Computation
Paradigm?
NaokiKatohandHiroIto
Abstract Thischapterintroducesthe“sublinearcomputationparadigm.”Asublinear-
timealgorithmisanalgorithmthatrunsintimesublinearinthesizeoftheinstance
(input data). In other words, the running time is o(n), where n is 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
sometimesbeinadequatebecausetheymayrequiretoomuchtimeorcomputational
resources.Insuchcases,sublinear-timealgorithmsareexpectedtoworkwell.Wecall
this idea the “sublinear computation paradigm.” A research project named “Foun-
dations on Innovative Algorithms for Big Data (ABD),” in which this paradigm is
thecentralconcept,wasstartedundertheCRESTprogramoftheJapanScienceand
TechnologyAgency(JST)inOctober2014andconcludedinSeptember2021.This
bookmainlyintroducestheresultsofthisproject.
1.1 WeAreintheEraofBigData
Thetwenty-firstcenturycanbecalledtheeraofBigData.Thenumberofwebpages
on the Internet was estimated to be more than 1 trillion (=1012) in 2008 [22], and
thenumberofwebsitesgrowstentimesinthese10years[21].Thusthenumberof
webpages is estimated to be more than 10 trillion (=1013) now. If we assume that
106bytes(≈107bits)ofdataiscontainedinasinglewebpageonaverage,1thenthe
totalamountofthedatastoredontheInternetwouldbemorethan100exabits(=1020
bits)!Thevariousactionsthateveryoneperformsarecollectedbyoursmartphones
andarestoredinthememoryofstoragedevicesaroundtheworld.Theremarkable
developmentofcomputermemoryhasmadeitpossibletostorethisinformation.
1Notethatone1080×1920pixeldigitalphotoconsistsofmorethan2×106pixels.
N.Katoh
UniversityofHyogo,8-2-1Gakuennishi-machi,Nishi-ku,Kobe,Hyogo651-2197,Japan
e-mail:[e-mail]
B
H.Ito( )
TheUniversityofElectro-Communications,1-5-1Chofugaoka,Chofu,Tokyo182-8585,Japan
e-mail:[e-mail]
©TheAuthor(s)2022 3
N.Katohetal.(eds.),SublinearComputationParadigm,
https://doi.org/10.1007/978-981-16-4095-7_1