236664

Advanced Topics in Biological Computing

236613

Advanced Topics in Cryptology

236663

Algorithmic Game Theory

Spring 2022

Inbal Talgam-Cohen

Mondays 10:30-13:30

An introductory course to the topic of Algorithmic Game Theory, the study of algorithms coupled with incentives. In light of the growing influence of algorithms on the economy and society, algorithm design must take into account the interaction with strategic players on top of traditional considerations like runtime complexity. As a prime example think of eBay auctions, which solicit bids from self-interested buyers.

The first half of the course will be dedicated to mechanism design, the science of designing such online auctions and markets. In the second half we will discuss the fundamental notion of equilibrium, including reaching it through centralized computation and decentralized learning.

Time: Mondays 10:30-12:30 (lecture) + Mondays 12:30-13:30 (recitation by Konstantin Zabarnyi)

Prerequisites: Algorithms 1

236359

Algorithms 2

Spring 2022

Seffi Naor

Tue 10:30-12:30, 13:30-14:30

This course is the natural follow-up to the basic algorithms course. We will consider basic topics and fundamental techniques in the theory of algorithms, such as randomization and algebraic tools. Possible topics include network flow, cuts in graphs, matchings, linear programming, approximation algorithms, and online algorithms.

Prerequisites: Algorithms

236646

Constraint Satisfaction Problems

Spring 2022

Yuval Filmus

Sunday, 12:30–14:30

Taub 4

We will discuss three main topics:

– Schaefer’s theorem, which shows that any Boolean CSP is either in P or NP-complete.

– Hardness of approximation: we will find the inapproximability thresholds for MAX-3LIN and for MAX-CUT.

– Proof complexity: we will show that some CNFs, including random ones, are hard to refute in Resolution.

If time permits, we will discuss a few more minor topics.

Prerequisites: Algorithms, Probability Theory

236755

Distributed Algorithms

Spring 2022

Hagit Attiya

Sunday 14:30-16:30, Tuesday 15:30-16:30

The course deals with design of algorithms for multi-processor systems, and analysis of their complexity; study of basic problems in such systems; lower bounds and impossibility results. Specific topics include: Mutual exclusion and resource allocation, agreement problems(Byzantine generals’ problem, approximate agreement, etc.), clock synchronization and logical clocks, broadcast and multicast, lock-free synchronization and concurrent data structures.

Previous:

236377

Distributed Graph Algorithms

Spring 2022

Keren Censor-Hillel

Wednesday, 10:30-12:30, 14:30-15:30

This course gives an introduction to distributed graph algorithms.

We will see various models of computation and the basic problems in this field.

We will study both algorithms and lower bounds.

This is an algorithmic/mathematical course.

There will be no final exam. The grade will be composed by 3-4 home assignments (submissions in singles) and a final project (submissions in pairs).

Prerequisites: Probability Theory, Algorithms, Computability (צמוד)

Previous:

Spring 2020

236377

Keren Censor-Hillel

236304

Logic for Computer Science 2

Spring 2022

Michael Kaminsky

Tuesday, 10:30–13:30

The main topics of the course are Gödel’s incompleteness theorems (including an axiomatic system for arithmetic, basics of recursion theory and Church’s thesis), set theory (axiomatic and combinatorial foundations of set theory as a basis for math), and modal logic (Kripke models, completeness theorems and connection to computer science).

For more information, please contact Professor Michael Kaminski.

Prerequisites: Logic, Computability (recommended, not obligatory)

236991

Project in Quantum Computing

236621

The Metric Method and its Algorithmic Applications

Spring 2022

Roy Schwartz

Monday 13:30-14:30, 15:30-17:30

Taub 5

The metric method is a powerful tool that has been used extensively in the last two decades in the design and analysis of algorithms.

This course will survey some of the basic techniques in the metric approach, as well as its applications to various topics such as: clustering and graph cuts, balanced graph partitioning, network routing, and online algorithms.

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Topics:

- Low distortion embeddings
- Approximate min multicut and max multicommodity flow
- Region growing and spreading metrics
- Approximating metrics by tree metrics
- Oblivious routing and approximating cuts by trees
- Metrics of negative type, random projections and measure concentration

Lecture: Monday 15:30-17:30 (Roy Schwartz)

Tutorial: Monday 13:30-14:30 (Dor Katzelnick)

Prerequisites: Algorithms 1, Computability, Probability Theory

The course will cover advanced algorithmic techniques developed for solving various (discrete) optimization problems. We will discuss linear programming, semidefinite programming, convex programming, and more. We will see applications of these techniques to a variety of applications, e.g., developing approximation algorithms for NP-hard problems, coloring (optimally) perfect graphs. Connections to learning theory will also be discussed.

Requirements: grades will be determined based on homework assignments.

Prerequisites: Algorithms 1, Computability, and an introductory course in probability.

Submodular functions, which capture the property of diminishing returns, are ubiquitous in various disciplines, including combinatorics, graph theory, machine learning, economics, algorithmic game theory, and information theory. The family of submodular maximization and minimization problems is a prime example of a unified approach that captures both well-known classic problems, e.g., Max-Cut, Max-DiCut, and Generalized Assignment, and real-world applications in diverse settings, e.g., information gathering, image segmentation, viral marketing in social networks, and recommendation systems. This course deals with the algorithmic foundations of submodular optimization, focusing on basic problems and algorithmic techniques.

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Topics:

- Introduction to submodularity.
- Submodular maximization with a cardinality constraint.
- Unconstrained submodular maximization.
- Introduction to matroids.
- Continuous extensions of submodular functions.
- Solving the multilinear relaxation.
- Rounding methods (pipage and swap rounding).
- Submodular minimization.
- The submodular multiway partition problem.

Staff and Times:

Monday 14:30-16:30 (lecture) – Roy Schwartz

Monday 13:30-14:30 (tutorial) – Dor Katzelnick

Prerequisites: Algorithms 1, Theory of Computation, Probability

In classic complexity theory, coping with NP-hard optimization problems often translates to the following fundamental question: “What is the best approximate solution that we can get in polynomial time?” We will present basic techniques for the design and analysis of approximation algorithms.

This includes combinatorial techniques (such as local search and local ratio) and techniques based on linear programming. We will demonstrate the use of these techniques for solving packing and scheduling problems, as well as problems on graphs.

Prerequisites: Introduction to Algorithms (234247), Theory of Computation (236343)

We will study basic mathematical models in machine learning, including supervised learning, online learning, interactive learning, and distribution learning.

We will focus on combinatorial characterizations of the complexity of learning.

The course requires mathematical maturity and will involve discussions about open problems and active research directions.

For student who attended the class with Shay in the last semester:

This semester we will cover different topics (in particular we will begin with the online learning model).

Also, notice the course number is different from that of last semester, so one can get credit for both classes.

Prerequisites: Combinatorics, Probability Theory.

**Definability **deals with the expressive power of description languages which are used in program specification, databases and axiomatic mathematics. These languages include Regular Expressions, First Order Logic, Relational Algebra, Second Order Logic and various Temporal and Modal Logics.

**Computability **deals with computations and the resources needed to execute them in various models of computations. These include Finite Automata, Turing Machines, Register Machines, and the like.

The course deals with the interplay between definability in various descriptive languages and computability with various computing devices. It brings together theoretical aspects of Database Theory, Computability Theory, Complexity Theory and Logic.

The course can be given in English if required. The slides are in English.

Prerequisites: Some knowledge of basic logic and computability is recommended.

Probabilistic methods have become a cornerstone of combinatorial theory, while probabilistic algorithms have become central to computer science.

This course introduces an array of already-classical and more modern probabilistic methods, along with their applications to math and CS. The course is centered on proof techniques and problem solving. Among the covered topics: basic methods, concentration inequalities, martingales, the local lemma, information entropy.

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Lecture Sunday 14:30-16:30,

Tutorial – TBA.

The course will be given in Hebrew.

Prerequisites: Probability Theory, Algorithms

The topic of the seminar is Algorithms for Constrained Resource Allocation.

We will review new variants of classic resource allocation problems arising in modern computing paradigms (such as Clouds and large data centers), and the challenges they present from algorithmic viewpoint.

Background material on approximation techniques for resource allocation problems which are known to be hard to solve will be presented in several introductory lectures at the beginning of the seminar.

Prerequisites: Theory of Computation (236343)

Machine learning often involves and affects people – a.k.a. “strategic agents” – who have interests, preferences and rights. This seminar covers recent research in the interdisciplinary questions that arise from this combination. Main topics include: Economic mechanisms and learning; strategic classification; incentivizing exploration; fairness in automatic decision making; and more.

Prerequisites: Algorithms 1

Useful but not required: Probability Theory, Learning Theory, Algorithmic Game Theory

The course will focus on topics related to complexity classes (quantum and classical), sophisticated algorithms, and cryptography.

Our goal is to reach an understanding of the potentially exponential advantage of quantum computing over classical computing in the near future and in the far future.

Prerequisites: Quantum computing or Complexity theory (may be taken in parallel)

Spring 2020

236640

Tal Mor

The course will focus on topics related to the origins of life and in particular the origins of the genetic code.

As we all know when we see a code – someone wrote it; With one exception – the genetic code.

Relying on the notion of “autocatalytic sets” we shall explore this topic.

Prerequisites: Biology 1, Algorithms 1

The use of mathematical programming is of paramount importance to the design and analysis of algorithms in general, and approximation algorithms in particular. While linear programming (LP) is the prototypical type of mathematical programming that is utilized, non-linear mathematical programming is also vastly used. This course will focus mainly on semi-definite programming (SDP) and survey its basic uses in the design and analysis of approximation algorithms as well as its applications to various topics such as: graph coloring, satisfiability, graph cuts, and clustering.

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Topics:

- Introduction to semi-definite programming
- The Max Cut problem
- Maximization of quadratic forms and Grothendieck’s inequality
- Correlation clustering
- Satisfiability and Max-SAT
- Graph coloring
- Lovász theta function
- Dimension reduction
- Metrics of negative type and random projections

Lecture: Monday 15:30-17:30 (Roy Schwartz)

Tutorial: Monday 13:30-14:30 (Dor Katzelnick)

Prerequisites: Algorithms 1, Computability, Probability Theory

Boolean function analysis is a set of tools coming from probability theory and functional analysis, with applications to theoretical computer science and combinatorics. The course is based, in large part, on the excellent monograph *Analysis of Boolean functions* by Ryan O’Donnell.

Grading is based on homework and a final project.

Prerequisites: Probability Theory

We will study basic mathematical models in machine learning, including supervised learning, online learning, interactive learning, and distribution learning.

We will focus on combinatorial characterizations of the complexity of learning.

The course requires mathematical maturity and will involve discussions about open problems and active research directions.

Prerequisites: Combinatorics and Probability Theory.

Basic topics in theoretical cryptography.

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- One-way functions and hard-core predicates.
- Definition and implementation of

secure encryption schemes. - Pseudorandom bit generators.
- Unforgeable signature schemes.
- Zero-knowledge interactive proof systems.
- Design of cryptographic protocols.

Suppose we are interested in figuring out whether a given input satisfies a given property, but we are only allowed to read a small part of the input. Can we still solve the problem, at least approximately? In many cases the answer is positive: it is possible to distinguish, with high probability, between inputs satisfying the property and inputs which are far from every input satisfying it. Such algorithms are known as *property testers*.

Prerequisites: Probability Theory, Algorithms

The first three lectures will serve as an introduction to approximation algorithms, via linear programming.

In the fourth lecture we will explore primal-dual techniques, and in the fifth the competing methodology, local ratio.

During the rest of the semester we will encounter many different applications to various optimization problems, such as vertex cover, set cover, Steiner trees, cycle cover, assignment problem, resource allocation, and more.

Proof-systems are at the very heart of theoretical computer science. For example the P vs NP question asks whether every statement that someone can prove to you, you could have actually solved by yourself.

In this course we will discuss advanced proof-systems such as:

* Interactive proofs, which are a natural generalization of NP proofs in which the verifier can interact with the prover.

* Zero-knowledge proofs, which allow one to prove the correctness of a statement without revealing anything else.

* Probabilistically Checkable Proofs (PCPs), which are proofs that can be verified by reading only a small number of bits.

* Doubly efficient proofs, which allow one to delegate expensive computations to an untrusted server.

Requirements: roughly 3 homework assignments and an exam.

Prerequisites: Computability

Winter 2020/2021

236601

Ron Rothblum

Communication complexity studies the number of bits that should be exchanged in order to perform a computation whose input is distributed among two or more parties. This is studied under a spectrum of computational models: deterministic, non-deterministic, randomized etc.

Beyond the immediate implications that such questions have to understanding distributed computations, we will present various surprising applications to seemingly unrelated questions, mostly in Complexity Theory.

The course will use methods from Combinatorics, Probability Theory and Algebra.

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Prerequisites:

Formally: “Complexity Theory” (236313) and a course in probability

(104034 or 094412).

Students with strong theory interests and the course “Computability Theory” (236343) can contact the lecturer for participation.

Prerequisites: Complexity Theory, Probability

The topic of this course is uncertainty in algorithms. Given a computational problem, the traditional design and analysis of algorithms assumes that complete knowledge of the input is known in advance. However, this is not the case in many applications, including resource management and allocation, data structures, and game dynamics. In these scenarios making decisions in the face of uncertainty is of major importance. Take, for example, managing a cache memory; when there is a page miss, the decision which page to evict from the cache is made without knowing future requests for pages.

In the course we will go over advanced techniques developed in recent years for dealing with such settings, where information about the future is unavailable or limited. We will mainly focus on competitive analysis of online algorithms and online learning, and study surprising connections between them. We will see how techniques from linear programming and convex optimization are useful for developing online algorithms.

Prerequisites: Algorithms 1, Theory of Computation, Introduction to Probability

This course will cover various advanced aspects of zero-knowledge proofs including:

1. Definitions, basic constructions and ZKP for NP.

2. Characterization of statistical zero-knowledge.

3. Non-interactive zero-knowledge.

4. A study of various efficiency aspects of zero-knowledge proofs.

Property testing algorithms are used to decide if some mathematical object (such as a graph or a Boolean function) has a “global” property, or is “far” from having this property, using only a small number of “local” queries to the object.

Prerequisites: Probability Theory

Course covering a wide range of topics in complexity theory, such as space complexity, the polynomial hierarchy, probabilistic computation, interactive proofs, circuit complexity, and more.

Prerequisites: Computability

This is a seminar course on combinatorial optimization. The course will focus on two different methodologies: local ratio and primal-dual.

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The first three lectures will serve as an introduction to approximation algorithms, via linear programming.

In the fourth lecture we will explore primal-dual techniques, and in the fifth the competing methodology, local ratio.

During the rest of the semester we will encounter many different applications to various optimization problems, such as vertex cover, set cover, Steiner trees, cycle cover, assignment problem, resource allocation, and more.

Prerequisites: Algorithms

Basic course on the theory of random graphs, focusing on the Erdős–Rényi model. Based on the nice Introduction to Random Graphs by Frieze and Karoński.

Grading is based on homework and a final project.

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Possible topics:

- Evolution of random graphs (appearance of giant component).
- Connectivity threshold.
- Subgraph thresholds and distributions.
- Clique number and chromatic number.
- Planted clique.
- Expanders.
- Random regular graphs.

Prerequisites: Linear Algebra, Probability Theory

Topics in pseudorandomness.

Discovery-based class, on a variety of topics. Students work in groups on handouts, with online help from the lecturer.

Grading based on final project.

Prerequisites: Probability Theory

Algorithms involving numbers, polynomials and matrices: FFT, fast integer multiplication, fast matrix multiplication, primality testing, integer factorization.

Prerequisites: Linear Algebra, Probability Theory