Lecture |
Subject |
Material |
References |
0 |
Introduction to the course |
slides |
- |
1 |
Basics of algorithm analysis |
slides |
- |
2 |
Sublinear time algorithms, estimating the average degree |
slides |
U Feige. On sums of independent random variables
with unbounded variance and estimating the average degree in a graph. |
3 |
Concentration bounds (Chebyshev and Chernoff) |
slides |
See Nick Harvey's notes on Chernoff bound. Benjamin Doerr, Probabilistic Tools. |
4 |
Estimating the average degree, continued |
slides |
A. Czumaj and C. Sohler, sublinear time algorithms (survey) |
5 |
Estimating the number of connected components |
slides |
B. Chazelle, R. Rubinfeld, and L. Trevisan.
approximating the minimum spanning tree weight in
sublinear time. 2005. |
6 |
Approximate median, k-median clustering |
slides |
- |
7 |
k-median clustering via sampling |
slides |
Mishra, Oblinger, Pitt. kmedian clustering in sublinear time. |
8 |
Estimating metric space properties via sampling |
slides |
P. Indyk. Sublinear time algorithms for metric space problems. |
- |
Happy Nowruz! |
- |
- |
9 |
Dimensionality reduction: Johnson-Lindenstrauss lemma |
slides |
Johnson, Lindenstrauss. extensions of Lipschitz mappings into a Hilbert space, 1984.
See also David Witmer's notes for missing details. |
10 |
Data stream model: frequency moments |
slides |
Alon, Matias, Szegedy. Space complexity of approximating the frequency moments. |
11 |
k-wise independence, distinct elements |
slides |
See Bernhard Haeupler's notes on k-wise independence. Alon, Matias, Szegedy's paper. |
12 |
Algorithms for heavy hitters |
slides |
J. Misra and D. Gries. Finding repeated elements. 1982. |
13 |
CountMin data structure |
slides |
Cormode and Muthukrishnan. An improved data stream summary:
The Count-Min sketch and its applications. |
14 |
Sketching, Mergeable summaries |
slides |
- |
15 |
Sparse recovery, L0 sampling |
slides |
Cormode and Jowhari. Lp sampling and its applications: a survey. 2019. |
16 |
Graph sketches, dynamic spanning forest |
slides |
Ahn, Guha and McGregor. Analyzing graph structure via linear measurements. 2012 |
17 |
Space lower bounds |
slides |
- |
18 |
Parallel computing and big data |
slides |
See Alex Andoni's notes on algorithms for massive data. Mohsen Ghaffari, massively parallel algorithms. |
19 |
Massively Parallel Computing, maximal matching |
slides |
Mohsen Ghaffari, massively parallel algorithms. |
20 |
Massively Parallel Computing, sorting |
slides |
See Alex Andoni's notes on algorithms for massive data. |
21 |
Three practice problems |
- |
- |
22 |
Solutions for practice problems |
- |
- |
23 |
Subspace embedding and least square regression |
slides |
D. Woodruff. sketching as a tool for numerical linear algebra |