Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Academic calendar
The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.
Course calendar
The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..
Period | From | To |
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I semestre | Oct 1, 2018 | Jan 31, 2019 |
II semestre | Mar 4, 2019 | Jun 14, 2019 |
Session | From | To |
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Sessione invernale d'esame | Feb 1, 2019 | Feb 28, 2019 |
Sessione estiva d'esame | Jun 17, 2019 | Jul 31, 2019 |
Sessione autunnale d'esame | Sep 2, 2019 | Sep 30, 2019 |
Session | From | To |
---|---|---|
Sessione Estiva | Jul 18, 2019 | Jul 18, 2019 |
Sessione Autunnale | Oct 17, 2019 | Oct 17, 2019 |
Sessione Invernale | Mar 18, 2020 | Mar 18, 2020 |
Period | From | To |
---|---|---|
Sospensione dell'attività didattica | Nov 2, 2018 | Nov 3, 2018 |
Vacanze di Natale | Dec 24, 2018 | Jan 6, 2019 |
Vacanze di Pasqua | Apr 19, 2019 | Apr 28, 2019 |
Festa del Santo Patrono | May 21, 2019 | May 21, 2019 |
Vacanze estive | Aug 5, 2019 | Aug 18, 2019 |
Exam calendar
Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.
To view all the exam sessions available, please use the Exam dashboard on ESSE3.
If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.
Should you have any doubts or questions, please check the Enrollment FAQs
Academic staff
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2019/2020
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Algorithms - COMPLESSITÀ (2018/2019)
Teaching code
4S02709
Teacher
Credits
6
Language
Italian
Scientific Disciplinary Sector (SSD)
ING-INF/05 - INFORMATION PROCESSING SYSTEMS
Period
II semestre dal Mar 4, 2019 al Jun 14, 2019.
To show the organization of the course that includes this module, follow this link: Course organization
Learning outcomes
The aim of the course is to provide the foundations of computational complexity theory. The focus will be on: the theory of NP-completeness; approximation algorithms and basic approaches for the analysis of the approximation guarantee of algorithms for hard problems.
The students who have successfully attended the course will be able to precisely formalize a computational problem, also in a research context, and analyze the computational resources its solution requires.
With the skills and knowledge acquired, students will be able to employ reductions, standard techniques in complexity theory, to analyze the structural properties of computational problems and identify possible alternative approaches (approximation, parameterization) in the absence of (provably) efficient solutions
After attending the course the students will be able to: classify intractable computational problems; understand and verify a formal proof; read and understand a scientific article where a new algorithm is presented together with the analysis of its computational complexity.
Program
Computational models, computational resources, efficient algorithms and tractable problems.
Relationships among computational problems. Polynomial reductions of one problem into another. The classes P, NP, co-NP. Notion of completeness. Proofs od NP-completeness: Cook's theorem; proofs of completeness using appropriate reductions. Search and Decision Problems. Self-Reducibility of NP-complete problems and existence of non-selfreducible problems. Recap of basic notions of computability: Turing Machines and Diagonalization. Hierarchy theorems for time complexity classes. Separability of classes and the existence of intermediate problem under the hypothesis the P is not equal NP.
Space Complexity. Models and fundamental difference between the use of time resource and the space resource. The space complexity classes NL and L and their relationship with the time complexity class P. The centrality of the reachability problem for the study of space complexity. Completeness for space complexity classes: Log-space reductions; NL-completeness of reachability. Non-determinism and space complexity. Savitch theorem and Immelmann-Szelepcsenyi theorem. The classes PSPACE and NPSPACE. Examples of reductions to prove PSPACE-completeness.
Introduction to the approximation algorithms for optimisation problems. Examples of approximation algorithms. Classification of problems with respect to their approximabuility. The classes APX, PTAS, FPTAS. Notion of inapproximability; the gap technique to prove inapproximability results; examples of approximation preserving reductions. Examples of simple randomised algorithms in solving hard problems.
Recommended Prerequisites
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To attend the course in a productive way, a student should be confident with the following topics:
1. Basic data structures as list, stack, queue, tree, heap.
2. Graph representation and fundamental graph algorithms:
2.1 Graph visit: BFS, DFS.
2.2 Topological ordering. Connected component.
2.3 Minimal spanning tree. Kruskal and Prim algorithm.
2.4 Single-source shortest path: Dijkstra algorithm and Bellman-Ford one.
2.5 All-pairs shortest path: Floyd-Warshall algorithm and Johnson one.
2.6 Max flow: Ford-Fulkerson algorithm.
A recommended book to revise the above topics is ``Introduction to Algorithms" di T. H. Cormen, C. E. Leiserson, R. L. Rivest e C. Stein (3 ed.).
Author | Title | Publishing house | Year | ISBN | Notes |
---|---|---|---|---|---|
J. Kleinberg, É. Tardos | Algorithm Design (Edizione 1) | Addison Wesley | 2006 | 978-0321295354 | |
Ingo Wegener | Complexity Theory | Springer | 2005 | ||
Michael Sipser | Introduction to the Theory of Computation | PWS | 1997 | 053494728X | |
Cristopher Moore, Stephan Mertens | The Nature of Computation | Oxford | 2011 |
Examination Methods
The exam verifies that the students have acquired sufficient understanding of the basic complexity classes and the necessary skills to analyse and classify a computational problem.
The exam consists of a written test with open questions. The test includes some mandatory exercises and a set of exercises among which the student can choose what to work on. The mandatory exercises are meant to evaluate the ability of the student to apply knowledge: reproducing (simple variants of) theoretical results and algorithms seen in class for classical problems. "Free-choice" exercises test the analytical skills acquired by the students to model "new" toy problems and analyse its computational complexity using reductions.
The grade for the module "complexity" is averaged (50%) with the grade for the module algorithm to determine the final grade.
Type D and Type F activities
Documents and news
- PIANO DIDATTICO LM-18 LM-32 (octet-stream, it, 17 KB, 21/09/18)
Modules not yet included
Career prospects
Module/Programme news
News for students
There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and soon also via the Univr app.
Graduation
Deadlines and administrative fulfilments
For deadlines, administrative fulfilments and notices on graduation sessions, please refer to the Graduation Sessions - Science and Engineering service.
Need to activate a thesis internship
For thesis-related internships, it is not always necessary to activate an internship through the Internship Office. For further information, please consult the dedicated document, which can be found in the 'Documents' section of the Internships and work orientation - Science e Engineering service.
Final examination regulations
List of thesis proposals
Attendance
As stated in the Teaching Regulations for the A.Y. 2022/2023, attendance at the course of study is not mandatory.