Course 2021-2022 a.y.

Introduction: Basic Notions and Theoretical Background

• Introduction, Turing Machines

• Stacks and Queues

• Array Resizing, Analysis of Algorithms, Asymptotic Notation, Exercises

Programming Paradigms and Data Structures

• Sorting, Comparison Sort Limits, Quicksort

• Master Theorem

• Binary Heaps, Binary sort, Binary Queues

• Binary Search Trees, Red-Black Trees

• Hash Tables

• Shortest Path Algorithms

• Dynamic Programming I

• Dynamic Programming II

• Algorithms for large scale data 

NP-Completeness

• NP-Completeness
• Approximation algorithms 

Optimization Algorithms

• Linear Programming
• Simplex algorithm
• Interior point methods
• Network flow algorithms, max flow min cuts I
• Network flow algorithms, max flow min cuts II
• Online decision making I
• Online decision making II 

Randomized Algorithms

• Randomized algorithms I
• Randomized algorithms II

• Understand the basic notions of algorithmic complexity, various design paradigms and data structures
• Develop an intuition about which problems are amenable to which kind of programming paradigm and relate this to common computational tasks like sorting and optimization
• Analyze the structure of advanced algorithmic schemes
• Understand optimization algorithms and the role of randomness
• Understand implications of NP-completeness

• Design algorithms using common paradigms and predict their scaling in terms of memory and computational resources
• Describe algorithms (possibliy developed by the students themselves) in pseudocode
• Read literature on algorithm design
• Develop algorithms for large scale difficult optimization problerms
• Show which problems cannot admit effiicient solutions

• Face-to-face lectures

Lectures.

The exam consists of a presentation and questions. The presentation can be either about a specific topic related to the course content, or about a project that the students complete before the exam. Several possible topics and projects will be proposed and students can also suggest their own ideas. The questions will be about the presentation and related topics that were covered in class.

The exam will test the students' ability to explain algorithms using the concepts learned in class and connect these concepts to specific problem instances. It will further test if the student can describe the scaling properties of the presented algorithms in terms of the mathematical notions of complexity learned in class. Depending on the topic of the presentation, the abilities of the students in the design of algorithms will be assessed and the understanding of related topics from the course will be tested.

• T.H. CORMEN, C.E. LEISERSON, R.L. RIVEST, et al., Introduction to Algorithms, MIT, 3rd edition.
• R. SEDGEWICK., and K. WAYNE.  Algorithms. Addison-wesley professional, 4th Edition.
• C. MOORE, S. MERTENS, The Nature of Computation, Oxford.
• R. MOTWANI, P. RAGHAVAN, Randomized algorithms, Cambridge University Press New York, NY, USA
• Bertsimas, Dimitris, and John N. Tsitsiklis. Introduction to linear optimization. Vol. 6. Belmont, MA: Athena Scientific, 1997
• Garey, Michael R., and David S. Johnson. Computers and intractability. Vol. 174. San Francisco: freeman, 1979.
• Lecture notes by the instructors.