#### Dr. Gianluca Della Vedova, Dr.ssa Raffaella Rizzi

#### University of Milano-Bicocca, Milano, Italy

This is the first PhD-level course on the design and the analysis of efficient algorithms, with a strong emphasis on theoretical aspects. The prerequisites are a very basic knowledge of graph theory and computational complexity, as well as a good understanding of undergraduate-level courses of algorithms, discrete mathematics, and operation research.

It is not necessary to have already taken a graduate-level course on algorithms.

The goal of the course is to give a broad coverage of the main techniques in algorithm design and analysis, so that the course can be useful also for a researcher in a different field. To this purpose, the computational problems tackled are among the most basic problems on strings and graphs, such as pattern matching, vertex cover and max cut.

In fact, anyone that deals with one of the following questions will find the course interesting.

- How can I cope with problems that are provably hard to solve exactly (i.e. are NP-hard)?
- How can I exploit the massive availability of CPUs?
- How can I query efficiently massive texts?

#### Lecture topics

- Parallel algorithms. (PRAM model, prefix sum algorithm, Map-Reduce)
- Randomized algorithms. (Karp-Rabin algorithm for pattern matching)
- Approximation algorithms. (Algorithms for Vertex Cover, Satisfiability, Max Cut. Approximation Complexity)
- Fixed-parameter algorithms. (Vertex cover)
- External-memory algorithms. (Parallel Disk Model, Sorting, B-trees)
- Streaming algorithms. (Heavy Hitters, Count-Min sketch, Reservoir sampling)
- Text algorithms. (Suffix trees, suffix arrays, LCP array, FM-index)

#### Exam

The exam will consists of some exercises that will be given during the course.

Collaboration is encouraged, but each student must write their own version of the solution.

#### Calendar:

Jan. 15, 10:30-12:30 – meeting room III floor, U14 (lecturer Gianluca Della Vedova)

Jan. 16, 10:30-12:30 – meeting room III floor, U14 (lecturer Gianluca Della Vedova)

Jan. 18, 10:30-12:30 – meeting room III floor, U14 (lecturer Raffaella Rizzi)

Jan. 22, 10:30-12:30 – meeting room I floor, U14 (lecturer Gianluca Della Vedova)

Jan. 29, 10:30-12:30 – meeting room III floor, U14 (lecturer Gianluca Della Vedova)

Jan. 30, 13:30-15:30 – meeting room III floor, U14 (lecturer Gianluca Della Vedova)

Feb. 1, 10:30-12:30 – meeting room III floor, U14 (lecturer Raffaella Rizzi)

Feb. 5, 10:30-12:30 – meeting room III floor, U14 (lecturer Gianluca Della Vedova)

Feb. 6, 10:30-12:30 – meeting room III floor, U14 (lecturer Gianluca Della Vedova)

Feb. 8, 10:30-12:30 – meeting room III floor, U14 (lecturer Raffaella Rizzi)