Sublinear Computation Paradigm 1st Edition by Naoki Katoh, Yuya Higashikawa, Hiro Ito, Atsuki Nagao, Tetsuo Shibuya, Adnan Sljoka, Kazuyuki Tanaka, Yushi Uno ISBN 9789811640940 9811640947

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ISBN 10: 9811640947
ISBN 13: 9789811640940
Author: Naoki Katoh, Yuya Higashikawa, Hiro Ito, Atsuki Nagao, Tetsuo Shibuya, Adnan Sljoka, Kazuyuki Tanaka, Yushi Uno

This open access book gives an overview of cutting-edge work on a new paradigm called the “sublinear computation paradigm,” which was proposed in the large multiyear academic research project “Foundations of Innovative Algorithms for Big Data.” That project ran from October 2014 to March 2020, in Japan. To handle the unprecedented explosion of big data sets in research, industry, and other areas of society, there is an urgent need to develop novel methods and approaches for big data analysis. To meet this need, innovative changes in algorithm theory for big data are being pursued. For example, polynomial-time algorithms have thus far been regarded as “fast,” but if a quadratic-time algorithm is applied to a petabyte-scale or larger big data set, problems are encountered in terms of computational resources or running time. To deal with this critical computational and algorithmic bottleneck, linear, sublinear, and constant time algorithms are required. The sublinear computation paradigm is proposed here in order to support innovation in the big data era. A foundation of innovative algorithms has been created by developing computational procedures, data structures, and modelling techniques for big data. The project is organized into three teams that focus on sublinear algorithms, sublinear data structures, and sublinear modelling. The work has provided high-level academic research results of strong computational and algorithmic interest, which are presented in this book.

Sublinear Computation Paradigm 1st Edition Table of contents:

Part I Introduction
1 What Is the Sublinear Computation Paradigm?
1.1 We Are in the Era of Big Data
1.2 Theory of Computational Complexity and Polynomial-Time Algorithms
1.3 Polynomial-Time Algorithms and Sublinear-Time Algorithms
1.3.1 A Brief History of Polynomial-Time Algorithms
1.3.2 Emergence of Sublinear-Time Algorithms
1.3.3 Property Testing and Parameter Testing
1.4 Ways to Decrease Computational Resources
1.4.1 Streaming Algorithms
1.4.2 Compression
1.4.3 Succinct Data Structures
1.5 Need for the Sublinear Computation Paradigm
1.5.1 Sublinear and Polynomial Computation Are Both Important
1.5.2 Research Project ABD
1.5.3 The Organization of This Book
References
Part II Sublinear Algorithms
2 Property Testing on Graphs and Games
2.1 Introduction
2.2 Basic Terms and Definitions for Property Testing
2.2.1 Graphs and the Three Models for Property Testing
2.2.2 Properties, Distances, and Testers
2.3 Important Known Results in Property Testing on Graphs
2.3.1 Results for the Dense-Graph Model
2.3.2 Results for the Bounded-Degree Model
2.3.3 Results for the General-Graph Model
2.4 Characterization of Testability on Bounded-Degree Digraphs
2.4.1 Bounded-Degree Model of Digraphs
2.4.2 Monotone Properties and Hereditary Properties
2.4.3 Characterizations
2.4.4 An Idea to Extend the Characterizations Beyond Monotone and Hereditary
2.5 Testable EXPTIME-Complete Games
2.5.1 Definitions
2.5.2 Testers for Generalized Chess, Shogi, and Xiangqi
2.6 Summary
References
3 Constant-Time Algorithms for Continuous Optimization Problems
3.1 Introduction
3.2 Graph Limit Theory
3.3 Quadratic Function Minimization
3.3.1 Proof of Theorem 3.1
3.4 Tensor Decomposition
3.4.1 Preliminaries
3.4.2 Proof of Theorem 3.2
3.4.3 Proof of Lemma 3.4
3.4.4 Proof of Lemma 3.5
References
4 Oracle-Based Primal-Dual Algorithms for Packing and Covering Semidefinite Programs
4.1 Packing and Covering Semidefinite Programs
4.2 Applications
4.2.1 SDP relaxation for Robust MaxCut
4.2.2 Mahalanobis Distance Learning
4.2.3 Related Work
4.3 General Framework for Packing-Covering SDPs
4.4 Scalar Algorithms
4.4.1 Scalar MWU Algorithm for (Packing-I)-(Covering-I)
4.4.2 Scalar Logarithmic Potential Algorithm For (Packing-I)–(Covering-I)
4.5 Matrix Algorithms
4.5.1 Matrix MWU Algorithm For (Covering-II)-(Packing-II)
4.5.2 Matrix Logarithmic Potential Algorithm For (Packing-I)-(Covering-I)
4.5.3 Matrix Logarithmic Potential Algorithm For (Packing-II)-(Covering-II)
References
5 Almost Linear Time Algorithms for Some Problems on Dynamic Flow Networks
5.1 Introduction
5.2 Preliminaries
5.3 Objective Functions
5.3.1 Objective Functions for the 1-Sink Problem
5.3.2 Objective Functions for k-Sink
5.4 Minmax k-Sink Problems on Paths
5.4.1 Feasibility Test
5.4.2 Solving the 1-Sink Problem
5.4.3 Parametric Search Method
5.4.4 Sorted Matrix Method
5.5 Minsum k-Sink Problems on Paths
5.5.1 Property of Aggregate Evacuation Time
5.5.2 Concave Monge Property
References
Part III Sublinear Data Structures
6 Information Processing on Compressed Data
6.1 Restructuring Compressed Data
6.1.1 Preliminaries
6.1.2 RLBWT to LZ77
6.1.3 Recompression on Grammar Compression
6.2 Privacy-Preserving Similarity Computation
6.2.1 Related Work
6.2.2 Edit Distance with Moves
6.2.3 Homomorphic Encryption
6.2.4 L2HE-Based Algorithm for Secure EDM
6.2.5 Result and Open Question
References
7 Compression and Pattern Matching
7.1 Introduction
7.2 History of Compressed Pattern Matching Research
7.3 Preliminaries
7.3.1 Definitions of Notation and Terms
7.3.2 Grammar Compression
7.4 Framework for Compressed Pattern Matching
7.4.1 KMP Method
7.4.2 Collage System
7.4.3 Pattern Matching on Collage Systems
7.5 Repair-VF
7.5.1 RePair
7.5.2 Outline of Repair-VF
7.6 MR-Repair
7.6.1 Maximal Repeats
7.6.2 MR Order
7.6.3 Algorithm
7.7 Conclusion
References
8 Orthogonal Range Search Data Structures
8.1 Introduction
8.1.1 Existing Work
8.1.2 Our Results
8.2 Preliminaries
8.2.1 Succinct Data Structures and Information-Theoretic Lower Bound
8.2.2 Assumptions on Point Sets
8.3 kd-Tree
8.3.1 Construction of kd-Trees
8.3.2 Range Search Algorithm
8.3.3 Complexity Analyses
8.4 Wavelet Tree
8.4.1 Construction
8.4.2 Range Search Algorithm
8.4.3 Complexity Analyses
8.5 Proposed Data Structure 1: Improved Query Time Complexity
8.5.1 Idea for Improving the Time Complexity of the kd-Tree
8.5.2 Index Construction
8.5.3 Range Search Algorithm
8.5.4 Complexity Analyses
8.6 Proposed Data Structure 2: Succinct and Practically Fast
8.6.1 Index Construction
8.6.2 Range Search Algorithm
8.6.3 Complexity Analyses
8.7 Conclusion
References
9 Enhanced RAM Simulation in Succinct Space
9.1 Introduction
9.2 Oblivious RAM
9.2.1 Problem
9.2.2 Existing Results
9.2.3 Tree-Based Methods
9.2.4 Succinct Construction
9.2.5 Open Problem
9.3 Wear Leveling
9.3.1 Problem
9.3.2 Security Refresh
9.3.3 Construction for Small Write Limit Cases
9.3.4 Open Problem
9.4 Conclusion
References
Part IV Sublinear Modelling
10 Review of Sublinear Modeling in Probabilistic Graphical Models by Statistical Mechanical Informatics and Statistical Machine Learning Theory
10.1 Introduction
10.2 Statistical Machine Learning
10.2.1 Bayesian Statistics and Maximization of Marginal Likelihood
10.2.2 Expectation-Maximization Algorithm
10.2.3 Expectation-Maximization Algorithm for Probabilistic Image Segmentations
10.3 Statistical Mechanical Informatics
10.3.1 Ising Model
10.3.2 Advanced Mean-Field Method
10.3.3 Free Energy Landscapes and Phase Transitions in the Thermodynamic Limit
10.3.4 Ising Model on a Complete Graph
10.3.5 Probabilistic Segmentation by Potts Prior and Loopy Belief Propagation
10.3.6 Real-Space Renormalization Group Method and Sublinear Modeling of Statistical Machine Learning
10.4 Quantum Statistical Machine Learning
10.4.1 Elementary Function and Differentiations of Hermitian Matrices
10.4.2 Minimization of Free Energy Functionals for Density Matrices
10.4.3 Tensor Products
10.4.4 Quantum Probabilistic Graphical Models and Quantum Expectation-Maximization Algorithm
10.4.5 Quantum Expectation-Maximization (EM) Algorithm for Probabilistic Image Segmentation
10.5 Quantum Statistical Mechanical Informatics
10.5.1 Advanced Mean-Field Methods for the Transverse Ising Model
10.5.2 Real-Space Renormalization Group Method for the Transverse Ising Model
10.5.3 Sublinear Modeling Using a Quantum Adaptive TAP Approach and Momentum Space Renormalization Group in the Transverse Ising Model
10.5.4 Suzuki-Trotter Decomposition in the Transverse Ising Model
10.6 Concluding Remarks
References
11 Empirical Bayes Method for Boltzmann Machines
11.1 Introduction
11.2 Boltzmann Machine with Prior Distributions
11.3 Empirical Bayes Method
11.4 Statistical Mechanical Analysis of Empirical Bayes Likelihood
11.4.1 Replica Method
11.4.2 Plefka Expansion
11.4.3 Algorithm for Hyperparameter Estimation
11.5 Demonstration
11.5.1 Gaussian Prior Case
11.5.2 Laplace Prior Case
11.6 Summary and Discussion
11.7 Appendices
11.7.1 Appendix 1: Gibbs Free Energy
11.7.2 Appendix 2: Coefficients of Plefka Expansion
References
12 Dynamical Analysis of Quantum Annealing
12.1 Quantum Ensembles and Their Dynamics
12.2 Quantum Monte Carlo Dynamics
12.3 Dynamical Replica Analysis
12.4 Simple Examples
12.4.1 Non-interacting Quantum Spins in a Uniform x Field
12.4.2 Ferromagnetic z-interactions and Uniform x and z Fields
12.5 Link Between Statics and Dynamics
12.6 Evolution on Adiabatically Separated Timescales
12.7 Discussion
References
13 Mean-Field Analysis of Sourlas Codes with Adiabatic Reverse Annealing
13.1 Introduction
13.2 Sourlas Codes Using Quantum Fluctuations
13.3 Replica Analysis for Adiabatic Reverse Annealing
13.4 Numerical Experiments
13.5 Summary
References
Part V Applications
14 Structural and Functional Analysis of Proteins Using Rigidity Theory
14.1 Introduction
14.2 Protein Structural Flexibility and Dynamics
14.2.1 Protein Flexibility and Dynamics Is Central to Protein Function
14.2.2 Techniques for Analysing and Predicting Protein Flexibility and Dynamics
14.3 Rigidity Theory
14.3.1 Combinatorial Rigidity Theory and the Molecular Theorem
14.4 Protein Flexibility, Dynamics, and Function Analysis with Rigidity Theory
14.4.1 FIRST and Rigid Cluster Decomposition
14.4.2 Large-Scale Rigidity and Flexibility Analysis
14.4.3 Protein Allostery Analysis with Rigidity Theory
14.4.4 Using Rigidity Theory to Simulate Protein Dynamics
14.5 Protein Structure Validation with Rigidity Theory
14.6 Conclusion
References
15 Optimization of Evacuation and Walking-Home Routes from Osaka City After a Nankai Megathrust Earthquake Using Road Network Big Data
15.1 Introduction
15.2 Quickest Evacuation Planning Problem
15.2.1 Dynamic Network
15.2.2 Time-Expanded Network
15.2.3 Algorithm for Solving Quickest Evacuation Planning Problem
15.3 Pedestrian Simulation Model
15.4 Data Preparation
15.4.1 Road Network
15.4.2 Tsunami Evacuation Buildings
15.4.3 Daytime Population
15.4.4 Decisions on Number of People Struggling to Return Home and Number of Evacuees
15.5 Simplifying and Restoring Large Road Network for Route Optimization
15.5.1 Simplification of Road Network
15.5.2 Restoring Optimized Routes on Original Road Network
15.6 Route Optimization Settings
15.6.1 Optimization Steps
15.6.2 Computational Conditions
15.7 Results of Route Optimization
15.7.1 Computational Times
15.7.2 Reproducibility of Restored Routes
15.7.3 Optimization Results
15.8 Conclusion
References
16 Stream-Based Lossless Data Compression
16.1 Introduction to Stream-Based Data Compression
16.2 Stream-Based Lossless Data Compression with Static Look-Up Table
16.2.1 Design of LCA-SLT
16.2.2 Implementation of LCA-SLT
16.2.3 Performance Evaluations
16.3 Stream-Based Lossless Data Compression with Dynamic Look-Up Table
16.3.1 Design of LCA-DLT
16.3.2 Implementation of LCA-DLT
16.3.3 Performance Evaluations
16.4 Optimization Techniques for LCA-DLT
16.4.1 Lazy Management of Look-Up Tables
16.4.2 Time-Sharing Multithreading on Compression
16.5 Related Works and Literatures
References

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Tags: Naoki Katoh, Yuya Higashikawa, Hiro Ito, Atsuki Nagao, Tetsuo Shibuya, Adnan Sljoka, Kazuyuki Tanaka, Yushi Uno, Sublinear Computation Paradigm