Prof. Roberto Grossi
Tutor: Dr. Filippo Geraci

Please register at http://piazza.com/unipi.it/fall2017/642aa for electronic discussion and other activities.

• Regarding your exam planning: I'll be on leave during 19.09.18-15.10.18 and 01.11.2018-28.02.19.
• Timetable: weekly timetable with changes: (Oct.5 → Oct.4, 14-16, I-Lab); (Oct.9 → Oct.2, 14-16, room A1); (Oct.10 → Oct.23, 14-16, room A1).
• Office hours: Thu. 14-17 or by appointment.

The advanced nature of this course focuses on developing algorithmic design skills, exposing the students to complex problems that cannot be directly handled by standard libraries (being aware that several basic algorithms and data structures are already covered by the libraries of modern programming languages), thus requiring a significant effort in problem solving. These problems involve all basic data types, such as integers, strings, (geometric) points, trees and graphs as a starting point. The syllabus is structured to highlight the applicative situations in which the corresponding algorithms can be successfully employed, making references to software applications and libraries. The level of detail in each argument can change year-by-year, and will be decided according to requests coming from other courses in the curriculum and/or specific issues arising in, possibly novel, applicative scenarios.

Written exam:

1. choose one of the topics discussed in class
2. write a very short to-do list and ask the instructor for approval
3. if the instructor suggests some mods, modify the to-do list according to the instructor's comments and repeat step 2
4. if the chosen topic and the to-do list are approved, expand the to-do list into a more detailed to-do list and repeat step 3
5. make a written report in English and submit it to the instructor (recall to add at least 20% new content, when compared to what seen in class)
6. meet the instructor to read together the report and get some comments on it
7. make the necessary mods

Suggested reading: some useful tips for scientific writing in English (first two sections) by J.S. Vitter.

Example of interaction: student and instructor discussing the report's content and structure.

Oral exam: topics discussed in class, please read the references in the notes.

Caveat: Several topics are the outcome of recent advancements in the field, and thus the course material mostly consists in research papers or book chapters.

Randomization is a powerful tool to solve large-scale problems. After introducing the concept of randomized algorithms and hashing, we consider some applications, such as data streaming algorithms, 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.]

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.

• Some of the screen snapshots shown during the classes.

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

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