# Advanced Algorithms, ETH Zurich, Fall 2020

- Instructor: Mohsen Ghaffari
- Teaching Assistants: Saeed Ilchi, Julian Portmann, and Vaclav Rozhon
- Units: 3V+2U+3A, 9 Credits
- Lecture Time & Place: Wednesdays 09:00-12:00 (online, see the course moodle for zoom link)
- Exercise Session Time & Place: Fridays 10:00-12:00 (online, see the course moodle for zoom link)
- Office Hours: By appointment/email
- Moodle: Advanced Algorithms 2020 on Moodle
- Prerequisite: Sufficient comfort with both (A) Algorithm Design & Analysis and (B) Probability & Basic Inequalities.

For instance, having passed the course Algorithms, Probability, and Computing (APC) is highly recommended, though not required formally.

If you're not sure whether you're ready for this class or not, please try Problem Set 00 and consult the instructor. - Other Links: Information on the Course Catalogue of ETH Zurich

Grading: Two graded homeworks 40%, and a 3-hour final exam 60%.

Homeworks, Problem Sets, and Exercise Sessions: During the semester, we will provide some specially-marked graded homeworks. Each of these graded homeworks will account for 20% of your grade.
You should submit your solutions, which __must be typeset in LaTeX__, via moodle. We will send you more detailed instructions via email.
Moreover, we will regularly have other problem sets, roughly one per lecture. You do not need to hand in their solutions.
However, we recommed that you try to solve all of these problems on your own, and seek help from the assistants, if needed. These problem sets will be discussed during the exercise sessions.
The exercise sessions are an indispensable part of the course -- the material covered in them will be included in the final exam and we strongly recommend attending them.

## Lecture Notes:Here are the for this course, but please keep in mind that the lecture notes will be updated throughout the semester.
Please see the course moodle for the video recordings of the lectures, and also for the handwritten notes (from the shared screen on the zoom session).
lecture notes |

## Topic List (14 ⨉ 3-hour lectures, in 5 blocks)

The following shows the schedule of the course in the 2020 edition. The precise schedule and content will be updated throughout the semester. Hollow bullet points indicate additional sources and optional material.

### Block 1: Basics of Approximation Algorithms

- (16.09) Lecture 01: Greedy --- Set Cover, Vertex Cover, and Knapsack via Dynamic Programming
- Chapters 1-2, 8-10 in Vazirani's Book on Approximation Algorithms
- Chapters 1-3 in Williamson & Shmoys's Book on Approximation Algorithms
- Lecture 13 of Demaine and Karger (6.854 Advanced Algorithms, MIT, Fall 2003)
- Lectures 1-3 of Svensson (Approximation Algorithms and Hardness of Approximation, EPFL, Spring 2013)

- (23.09) Lecture 02: PTAS and FPTAS --- Knapsack and Bin Packing, [+ Optional: Minimum Makespan Scheduling]
- Chapters 8-10 in Vazirani's Book on Approximation Algorithms
- Chapter 3 in Williamson & Shmoys's Book on Approximation Algorithms
- Lectures 12-13 of Demaine and Karger (6.854 Advanced Algorithms, MIT, Fall 2003)
- Lecture 3 of Svensson (Approximation Algorithms and Hardness of Approximation, EPFL, Spring 2013)

- (30.09) Lecture 03: FPRAS --- DNF Counting, [+ Optional: Network Reliability,] and Counting Graph Colorings
- Chapter 28 of Vazirani's Book on Approximation Algorithms
- The 1999 paper of Karger
- Lectures 10 & 11 of Sinclair (CS271 Randomness and Computation, Berkeley, Fall 2011)
- Lectures 14 of Sinclair (CS294 Markov Chain Monte Carlo: Foundations and Applications, Berkeley, Fall 2009)

- (07.10) Lecture 04: Rounding Linear Programs --- Vertex Cover and Set Cover, Congestion in Multi-Commodity Routing, Matching in Bipartite Graphs, [+ Optional: Scheduling on Unrelated Machines]
- Chapters 14 of Vazirani's Book on Approximation Algorithms
- Chapter 5.11 in Williamson & Shmoys's Book on Approximation Algorithms
- Section 4.3 in Motwani & Raghavan's Book
- Lectures 9 & 10 of Checkuri (CS 583, Approximation Algorithms, UIUC, Spring 2011)

### Block 2: Selected Topics in Approximation Algorithms

- (15.10) Lecture 05: Distance-Preserving Tree Embedding and Buy-at-Bulk Network Design
- The 1996 paper of Bartal
- The 2003 paper of Fakcharoenphol, Rao, and Talwar
- Sections 8.5 & 8.6 in Williamson & Shmoys's Book on Approximation Algorithms
- Lecture 14 of Gupta (15-859M, Randomized Algorithms, CMU, Spring 2011)
- Lectures 23 of Checkuri (CS 598, Approximation Algorithms, UIUC, Spring 2009)

- (21.10) Lecture 06: L1 Metric Embedding and Sparsest Cut
- Chapter 6 of the Lecture Notes
- Problem Set 6
- Graded Homework 1. Deadline: 11:59 pm on Nov 6 (submit via Moodle).

- Chapter 21 of Vazirani's Book on Approximation Algorithms
- Lectures 3 of Gupta and Ravi (15-859, Algorithmic Applications of Metric Embeddings, CMU, Fall 2003)
- Lectures 13 of Svensson (Approximation Algorithms and Hardness of Approximation, EPFL, Spring 2013)
- Lectures 19 of Gupta (CS 15-854B, Advanced Approximation Algorithms, CMU Spring 2008)
- Lectures 20 & 21 of Checkuri (CS 598, Approximation Algorithms, UIUC, Spring 2009)
- The 1995 paper of Linial, London, and Rabinovich
- A survey by Indyk on algorithmic applications of embeddings from 2001

- (28.10) Lecture 07: Cut-Preserving Tree Embedding, Oblivious Routing, and Balanced Cut
- Chapters 15.2 and 15.3 in Williamson & Shmoys's Book on Approximation Algorithms
- The 2008 paper of Raecke
- The 2009 paper of Anderson and Feige

- (04.11) Lecture 08: Multiplicative Weight Updates, Approximating Covering/Packing LPs, and Constructive Oblivious Routing
- Chapter 8 of the Lecture Notes. Sections 8.2 and 8.3 are incomplete. See the handwritten notes and zoom video on moodle, for now.
- Problem Set 8

- Lectures 16 and 17 of Gupta (15-859(E): Linear and Semidefinite Programming, CMU, Fall 2011)
- Lecture 4 of Vazirani and Rao (CS270, Algorithms, UC Berkeley, Spring 2011)
- Survey by Arora, Hazan, and Kale
- The 2008 paper of Raecke

### Block 3: Streaming & Sketching Algorithms

- (11.11) Lecture 09: Frequent Elements, Approximate Counting, and Distinct Elements, and Moment Estimations
- Lectures 1-3 of Nelson (CS 299r, Algorithms for Big Data, Harvard, Fall 2015)
- Weeks 11 & 12 of Nikolov (CSC473: Advanced Algorithm Design, Toronto, Winter 2017)
- Lectures 5 & 6 of Karger (6.854 Advanced Algorithms, MIT, Fall 2016)
- Lecture 7 of Krauthgamer and Naor (Randomized Algorithms, Weizmann Institute, Fall 2015)
- The 1996 paper of Alon, Matias, and Szegedy

- (18.11) Lecture 10: Connectivity via Graph Sketching
- Chapter 11 of the Lecture Notes
- No problem set -- This week's exercise session reviews Graded Homework 1.

- Lectures 13 and 16 of Indyk (6.895 Sketching, Streaming and Sublinear Space Algorithms, MIT, Fall 2007)
- Lecture 7 of Nelson (CS 299r, Algorithms for Big Data, Harvard, Fall 2015)
- The 2012 paper of Ahn, Guha, and McGregor
- Survey by McGregor

### Block 4: Graph Sparsification

- (25.11) Lecture 11: Distance-Preserving Graph Sparsification, i.e., Spanners
- Chapter 12 of the Lecture Notes
- Problem Set 10
- Graded Homework 2. Deadline: 11:59 pm on Dec 15 (submit via Moodle).

- Lectures 6 and 7 of Vassilevska Williams (CS 267, Graph Algorithms, Stanford, Spring 2016)
- The 1999 paper of Aingworth, Chekuri, Indyk, and Motwani
- The 2013 paper of Chechik
- The 2003 paper of Baswana and Sen

- (02.12) Lecture 12: Cut-Preserving Graph Sparsification
- The 1996 paper of Benczur and Karger
- Lecture 5 of Krauthgamer and Naor (Randomized Algorithms, Weizmann Institute, Fall 2015)
- Lecture 13 of Bansal (2WO08, Graphs and Algorithms, Eindhoven Univ. of Tech, Spring 2015)

### Block 5: Online Algorithms & Competitive Analysis

- (09.12) Lecture 13: Ski Rental, Lost Cow, Linear Search, and Paging
- Lectures 19 & 20 of Demaine and Karger (6.854 Advanced Algorithms, MIT, Fall 2003)
- Lecture 22 of Karger (6.854 Advanced Algorithms, MIT, Fall 2005)
- Lectures 14 and 15 of Blum (15-854 Approximation and Online Algorithms, CMU, Spring 2000)
- Lecture 22 of Gupta (15-850, Advanced Algorithms, CMU, Spring 2017)
- Chapters 1 to 4 of Borodin and El-Yaniv's Book on Online Computation and Competitive Analysis
- A survey by Irani on Competitive Analysis of Paging

- (16.12) Lecture 14: Paging, Yao's Principle, and k-Server
- Lecture 3 of Azar (0368.4041 Online and Approximation Algorithms, Tel Aviv University, Spring 2016)
- Chapter 10 of Borodin and El-Yaniv's Book on Online Computation and Competitive Analysis
- A survey by Koutsoupias on the k-Server Problem from 2009

### Additional Material:

**Basic Probability Inequalities:**Please make sure that you are comfortable with the basics of probability, e.g., Linearity of Expectation, Markov, Chebyshev, and Chernoff/Hoeffding. You might find the following sources useful: A handout by Avrim Blum and Anupam Gupta (15-859 Randomized Algorithms, CMU, Spring 2011), and another handout by Angelika Steger and Emo Welzl (Randomized Algorithms and Probabilistic Methods, ETH, Fall 2017).