CSE 597A Sublinear Algorithms1
Fall 2015

General Information

Time and location: Tuesday/Thursday 1:00PM-2:15PM, 121 Earth And Engr Sci
Instructor: Sofya Raskhodnikova
Office hours: Tuesdays, 2:30PM-3:30PM, IST 343F

Prerequisites

CSE 565; STAT 318 or MATH 318

Course description

This course will cover the design and analysis of algorithms that are restricted to run in sublinear time. Such algorithms are typically randomized and produce only approximate answers. A characteristic feature of sublinear algorithms is that they do not have time to access the entire input. Therefore, input representation and the model for accessing the input play an important role. We will study different models appropriate for sublinear algorithms. The course will cover sublinear algorithms discovered in a variety of areas, including graph theory, algebra, geometry, image analysis and discrete mathematics, and introduce many techniques that are applied to analyzing sublinear algorithms.

Grading

Students will be evaluated based on class participation, solutions to about 4 homework assignments, taking lecture notes about 2-3 times per person, and the final project.

Lectures

Lec Date Topics References Reading/Homework
1 Tu, Aug 25 Introduction. Basic models for sublinear-time computation. Simple examples of sublinear algorithms. (Slides for lectures 1 & 2 ) RS96, GGR98, Ras03, EKKRV00, Fis04 Ras03, Ras15
Th, Aug 27 No lecture; students are encouraged to attend the DIMACS workshop on sublinear algorithms
2 Tu, Sep 1 Properties of lists and functions. Testing if a list is sorted/Lipschitz and if a function is monotone. (See slides posted for previous lecture.) DGLRRS99, BGJRW09, Ras10, JR13
3 Th, Sep 3 Testing a bounded-degree graph is connected. Approximating the number of connected components and MST weight. (Slides ) GR02, CRT05 Homework 1 out; HW template files: Sample Homework Solution (pdf), Sample Homework Solution (latex), Example HW image, HW class file
4 Tu, Sep 8 Background on probability Handouts on probability by Dana Ron and from MIT lecture and recitation
5 Th, Sep 10 Discussion of HW 1. Methods for proving lower bounds: Yao's principle. (Slides for lectures 5 & 6 ) FLNRRS02
6 Tu, Sep 15 Discussion of course projects. Yao's principle (see slides posted for previous lecture). Homework 1 due
Th, Sep 17 No lecture
7 Tu, Sep 22 Methods for proving lower bounds: communication complexity. (Slides for lectures 7 & 8 ) BBM11 First project meeting
8 Th, Sep 24 Other models of sublinear time/space computation (see slides posted for previous lecture). Two-distribution version of Yao's Principle. Project proposal due (10 am on Angel); Homework 2 out
9 Tu, Sep 29 Application of Yao's Principle: limits of nonadaptive algorithms in the bounded-degree model. RS06
10 Th, Oct 1 Dense graphs: testing bipartiteness. GGR98, AK02
11 Tu, Oct 6 Dense graphs: finish testing bipartiteness. GGR98 Homework 2 due (10am on Angel)
12 Th, Oct 8 Image properties: Testing if an image is a half-plane under the uniform distribution. BMR
13 Tu, Oct 13 Image properties: learning and testing convexity under the uniform distribution. BMR
14 Th, Oct 15 Image properties: finish testing convexity under the uniform distribution.
15 Tu, Oct 20 A connection between proper learning and testing. Image properties: adaptive convexity tester. Alon02 Project progress reports due (10am on Angel); second project meeting
16 Th, Oct 22 Image properties: connectedness. GR08
17-19 Tu, Oct 27; Th, Oct 29; Tu, Nov 3 Dense graphs: approximating max-cut. GGR98
20 Th, Nov 5 Testing dense graphs: discuss characterization. Testing triangle-freeness. Regularity lemma. AFKS00
21 Tu, Nov 10 Testing triangle-freeness. Triangle-removal lemma. Homework 3 out
22 Th, Nov 12 Dense graphs: lower bound for testing triangle-freeness. Alon02
23 Tu, Nov 17 Approximating graph parameters: average degree GR08
24 Th, Nov 19 Approximating graph parameters GR08 HW3 due
25 Tu, Nov 24 Testing properties of functions: linearity. (Slides ) BLR93, BCHKS96
26 Th, Nov 26 Testing properties of functions: monotonicity and the Lipschitz property
27 Tu, Dec 1 Testing properties of functions: monotonicity and the Lipschitz property Project final reports due
28 Th, Dec 3 L_p-testing
29 Tu, Dec 8 Final project presentations
30 Th, Dec 10 Final project presentations

Lecture notes

Preamble and bib files; lecture notes wiki; lecture notes wiki from 2012

Notes themselves, possibly in a rough shape:

Lecture 3. Testing connectedness. Approximating the number of connected components and MST weight. pdf, tex

Miscellaneous

Resources on sublinear algorithms
Property testing review, open problems.
LaTeX
For tips on using latex to type homework, see these links. Homework template files: tex, pdf, cls, jpg.
Other Useful Programs
On Mac, emacs and Skim

Bibliography

Most papers from the list below can be downloaded from the Princeton archive or my webpage.

RS96 Ronitt Rubinfeld, Madhu Sudan, Robust Characterizations of Polynomials with Applications to Program Testing. SIAM Journal of Computing 1996.
GGR98 Oded Goldreich, Shafi Goldwasser, Dana Ron, Property Testing and its Connection to Learning and Approximation. Journal of ACM 1998, FOCS 1996.
Ras03 Sofya Raskhodnikova, Approximate Testing of Visual Properties. RANDOM-APPROX 2003.
Ras15 Sofya Raskhodnikova, Testing if an Array Is Sorted. Encyclopedia of Algorithms 2015.
RS06 Sofya Raskhodnikova, Adam Smith A Note on Adaptivity in Testing Properties of Bounded Degree Graphs. Electronic Colloquium on Computational Complexity, Report No. 89, 2006.
EKKRV00 Funda Erg√ľn, Sampath Kannan, Ravi Kumar, Ronitt Rubinfeld, Mahesh Viswanathan, Spot-Checkers. Journal of Computer System and Sciences 2000, STOC 1998.
Fis04 Eldar Fischer, On the strength of comparisons in property testing. Information and Computation 2004.
DGLRRS99 Yevgeniy Dodis, Oded Goldreich, Eric Lehman, Sofya Raskhodnikova, Dana Ron, Alex Samorodnitsky, Improved Testing Algorithms for Monotonicity. RANDOM-APPROX 1999.
BFJRW09 Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, David Woodruff, Transitive-Closure Spanners. SODA 2009.
Ras10 Sofya Raskhodnikova, Transitive-Closure Spanners: a Survey. In O. Goldreich, editor, Property Testing, LNCS 6390, LNCS State-of-the-Art Surveys, Springer, Heidelberg, 167--196, 2010.
JR13 Madhav Jha, Sofya Raskhodnikova, Testing and Reconstruction of Lipschitz Functions with Applications to Data Privacy. SIAM Journal on Computing 2013, STOC 11.
GR02 Oded Goldreich, Dana Ron, Property testing in bounded degree graphs. Algorithmica 2002, STOC 1997.
CRT05 Bernard Chazelle, Ronitt Rubinfeld, Luca Trevisan, Approximating the Minimum Spanning Tree Weight in Sublinear Time. SIAM Journal of Computing 2005, ICALP 2001.
FLNRRS02 Eldar Fischer, Eric Lehman, Ilan Newman, Sofya Raskhodnikova, Ronitt Rubinfeld, Alex Samorodnitsky Monotonicity Testing Over General Poset Domains. STOC 2002.
BBM11 Eric Blais, Joshua Brody, Kevin Matulef, Property Testing Lower Bounds via Communication Complexity. CCC 2011.
AK02 Noga Alon, Michael Krivelevich, Testing k-colorability. SIAM J. Discrete Math. 15 (2002), 211-227.
Alon02 Noga Alon, Testing subgraphs in large graphs. Random Structures and Algorithms 21 (2002), 359-370.
AFKS02 Noga Alon, Eldar Fischer, Michael Krivelevich, Mario Szegedy, Efficient testing of large graphs, Combinatorica 20 (2000), 451-476.
GT03 Oded Goldreich, Luca Trevisan, Three theorems regarding testing graph properties, Random Struct. Algorithms 23(1): 23-57 (2003)
GR08 Oded Goldreich, Dan Ron, Approximating average parameters of graphs, Random Struct. Algorithms 32(4): 473-493 (2008)
PaRo07 Michal Parnas, Dan Ron, Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms, Theor. Comput. Sci., 381(1-3):183--196 (2007)
NO08 Huy N. Nguyen and Krzysztof Onak, Constant-Time Approximation Algorithms via Local Improvements, FOCS (2008)
ORRR12 Krzysztof Onak, Dana Ron, Michal Rosen, and Ronitt Rubinfeld, A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size, In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1123--1131 (2012)
Ras99 Sofya Raskhodnikova, Monotonicity Testing, Master's Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1999
CS12 Deeparnab Chakrabarty, C. Seshadhri Optimal bounds for monotonicity and Lipschitz testing over the hypercube. ECCC, TR12-030, 2012.
BBBY12 Maria-Florina Balcan, Eric Blais, Avrim Blum, Liu Yang, Active Property Testing. Manuscript, 2012.
BLR93 Manuel Blum, Michael Luby, Ronitt Rubinfeld, Self-Testing/Correcting with Applications to Numerical Problems. Journal of Computer System and Sciences 1993, STOC 1990.
BCHKS96 Linearity testing in characteristic two. IEEE Transactions on Information Theory, Vol. 42, No. 6, pp. 1781--1795, 1996, FOCS 95.

1. The design of this course is partially supported by the National Science Foundation under Grant No. 0845701. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).