Prof. Roberto Grossi
Tutor: Dr. Filippo Geraci

• Results and scheduling of the oral examinations in the following days: Tue, Jan 12, 2016, at 9:00 in my office.
• New exercises (Dec. 15) added to the partial list of problems.
• Next terms: Jan. 20 at 9:00 in room L1; Feb. 10 at 9:00 in room L1.
• Office hours: Tue 14-16 (Dipartimento di Informatica)

We will study, design and analyze advanced algorithms and data structures for the efficient solution of combinatorial problems involving all basic data types, such as integers, strings, (geometric) points, trees and graphs. This course deepens and extends the algorithmic notions of students.

The syllabus is structured to highlight the applicative scenarios in which the studied algorithms and data structures can be successfully applied. The level of detail with which each argument will be dealt with can change year-by-year, and will be decided according to requests coming from other courses and/or specific issues arising in, possibly novel, applicative scenarios.

The advanced nature of this course focuses on developing algorithmic design skills. The students are exposed to complex problems that require a significant effort in problem solving. One “brainstorming” lecture per week is devoted to a full immersion in this activity, and it is highly recommend to attend it. The purpose is not that of teaching/learning further N algorithms, but to refine students' skills. The final written exam will be based on the topics discussed during the “brainstorming” lectures.

We like students that make mistakes in a constructive way, since this is the starting point of our brainstorming to drive their reasoning paths, thus learning by mistakes. We are interested in the route that leads to the algorithmic solution, rather than the solution itself. Regarding mistakes and intelligence, Alan Turing wrote in 1947 that “… if a machine is expected to be infallible, it cannot also be intelligent”. This is a motto for this class, with a kind invitation to express your own ideas even if they could be apparently wrong.

Please note that several topics are the outcome of recent advancement in algorithms and data structures, and thus most of the course material consists in research papers or book chapters.

Randomization is now a common powerful tool to solve large-scale problems. After introducing the concept of randomized algorithms and hashing, we apply them to solve data streaming problems, a field emerged in the last decade. Here data flow as a stream and one-pass algorithms with limited memory can process it. We focus on the count-min sketch paradigm and its applications. [Note: to refresh the basic notions on counting and probability, please refer to Appendix C in Cormen-Leiserson-Rivest-Stein's book “Introduction to Algorithms”, 3rd ed., MIT Press.]

Massive data sets are one of the key elements in our so-called big data society. In this scenario the design and analysis of algorithms and data structures adopt the external and cache-oblivious models, which take into account the memory hierarchy that provides performance to modern computers. We study basic problems on sorting and searching in these models, comparing the results with the classical RAM model of computation.

NP-hard problems are important but difficult to solve and no deterministic polynomial algorithms are currently known for them. Even basic problems, such as finding a simple path of vertices in a graph, are NP-hard. We discuss how to attack these problems (a) by counting and listing their solutions where the cost is proportional to the output (it can be exponential in the worst case but we only pay for what we get) and (b) by approximating their solutions with polynomial-time algorithms when the problem requires to minimize a cost or maximize a benefit. Most of the addressed problems are on graphs, which are popular representations for modern networked data.

• This is the final list of problems.
• Some of the screen snapshots shown during the classes.

• Access to unimap log (registro delle lezioni).
• Access to the course evaluation form (questionario studenti).

Examination of Dec. 16, 2015

Examination of Jan. 20, 2016

• 463883 27
• 468827 26
• 541769 18

Examination of Feb. 10, 2016

• 300759 21
• 459410 30
• 489617 29
• 493413 29
• 540574 11
• 541451 12
• 541769 27
• 541784 24