Spring 2012

**Time and location:** Tuesday/Thursday 1:00PM-2:15PM, 167 Willard Bldg
**Instructor:**
Sofya Raskhodnikova

**Office hours:** Tuesdays, 2:30PM-3:30PM, IST 343F

CSE 565; STAT 318 or MATH 318

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.

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.

Lec | Date | Topics | References | Handouts/Homework |
---|---|---|---|---|

1 | Tu, Jan 10 | Introduction. Basic models for sublinear-time computation. Simple examples of sublinear algorithms. (slides for lectures 1 & 2 ) | RS96, GGR98, Ras03, EKKRV00, Fis04 | General information |

2 | Th, Jan 12 | Properties of lists, functions, graphs. Testing if a list is sorted/Lipschitz, if a function is monotone, and if a bounded-degree graph is connected. (See slides posted for previous lecture.) | DGLRRS99, BGJRW09, Ras10, JR11, GR02 | |

3 | Tu, Jan 17 | Finished testing connectedness. Approximating the number of connected components and MST weight. (slides ) | GR02, CRT05 | |

4 | Th, Jan 19 | Background on probability | Handouts on probability by Dana Ron and from MIT lecture and recitation | Homework 1 out |

5 | Tu, Jan 24 | Methods for proving lower bounds: Yao's principle. (slides ) | FLNRRS02 | |

6 | Th, Jan 26 | Methods for proving lower bounds: communication complexity. Other models of sublinear time/space computation. Discussion of course projects. (slides ) | BBM11 | HW1 due |

7 | Tu, Jan 31 | Dense graphs: testing bipartiteness | GGR98, AK02 | First project meeting |

8 | Th, Feb 2 | Dense graphs: approximating max-cut | GGR98 | Project proposal due; Homework 2 out |

9 | Tu, Feb 7 | Dense graphs: Finish approximating max-cut. | GGR98 | |

10 | Th, Feb 9 | Testing dense graphs: discuss characterization. Testing triangle-freeness. Regularity lemma. | AFKS00 | |

11 | Tu, Feb 14 | Triangle-removal lemma | ||

12 | Th, Feb 16 | Dense graphs: lower bound for testing triangle-freeness. | Alon02 | Homework 2 due |

13 | Th, Feb 23 | In class problem solving: adaptivity in the dense-graph model | GT03 | |

14 | Tu, Feb 28 | Approximating graph parameters: average degree | GR08 | |

15 | Th, Mar 1 | Approximating Vertex Cover and distributed algorithms | PaRo07 | |

16 | Tu, Mar 13 | Approximating Vertex Cover and distributed algorithms | PaRo07, NO08, ORRR12 | |

17 | Th, Mar 15 | Testing monotonicity of functions: range reduction | DGLRRS99, Ras99 | |

18 | Tu, Mar 20 | Testing monotonicity of functions on hypergrids: dimension reduction | DGLRRS99, Ras99 | Project progress reports due |

19 | Th, Mar 22 | Properties defined by 2CNF formulas and testing monotonicity of functions on posets | FLNRRS02 | |

20 | Tu, Mar 27 | Induced matchings and a lower bound for testing monotonicity of functions on posets | FLNRRS02 | Homework 3 out |

21 | Th, Mar 29 | Finish the lower bound for testing monotonicity on posets: (s,t)-Rusza-Semeredi graphs | FLNRRS02 | |

22 | Tu, April 3 | Testing monotonicity of Boolean functions on hypergrids | DGLRRS99 | |

23 | Th, April 5 | Testing monotonicity of Boolean functions on hypergrids (part 2) | DGLRRS99 | Homework 3 due |

24 | Tu, April 10 | Resolution of monotonicity (and Lipschitz) testing conjectures | CS12 | |

25 | Th, April 12 | Talk by Avrim Blum: Active (and Passive) Property Testing | BBBY12 | Homework 3 due |

26 | Tu, Apr 17 | Testing linearity of functions. (slides ) | BLR93, BCHKS96 | Project final reports due |

27 | Tu, Apr 24 | Final project presentations | ||

28 | Th, Apr 26 | Final project presentations (in 222 IST) |

- 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

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. |

EKKRV00 | Funda Ergün, 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. |

JR11 | Madhav Jha, Sofya Raskhodnikova, Testing and Reconstruction of Lipschitz Functions with Applications to Data Privacy. FOCS 2011. |

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. |