This course deals with advanced topics in algorithm design and parallel programming.

The course is structured in two parts. The first part focuses on general methods and algorithms that are not usually covered by the course “Algoritmi e Principi dell’Informatica”, such as randomization, amortization, approximation algorithms, string searching/matching, etc.

The second part deals with parallel programming: Automatic vs. Manual Parallelization, Parallelizing Compilers, Parallel Patterns (map, reduce, scan, etc.), Partitioning (domain vs. functional decomposition), Communication (cost, latency, bandwidth, visibility, synchronization, etc.), Data Dependencies and Tools/languages such as OpenMP and MPI.

 An innovative teaching activity (1 CFU), Blended Learning & Flipped Classroom, is planned for some of the topics covered by the course.

Knowledge and understanding

Students will learn how to:

- develop advanced algorithms by analyzing their complexity and by exploiting randomized approaches,  randomized based data structures, dynamic programming, amortized analysis, competitive analysis, and approximate programming;

- design and analyze a parallel algorithm by exploiting parallel patterns, tools, and languages for parallel programming.

Applying knowledge and understanding

Given specific problems, students will be able to:

- understand complex problem descriptions;

- design algorithms and analyze their complexity;

- design and implement parallel algorithms;

- profile and fine-tune the performance of complex programs.

- understand where the pitfall and issues may come in (parallel) programming.

Making judgments

Given a relatively complex problem, students will be able to:

- define the relevant data sets required to judge the quality of the proposed solution;

- understand if the obtained performance is in line with the expected complexity;

- understand if the proposed solution scales well or not;

- understand where previous approaches are relevant or not for a given problem.

Communication

Students will learn to:

- present their work discussing the pros and cons of the proposed solution.

- present the existing state of the art by showing where it could be improved or where it is inconsistent; 

Lifelong learning skills

Students will understand how a complex algorithm, possibly parallel, has to be analyzed, designed, and assessed.

They will play with real problems, understanding where pitfalls may come when you move from a theoretical formulation down to an actual implementation considering existing tools and architectures.

Part I

Course Objectives and Introduction

Randomized algorithms: Las Vegas and Monte Carlo algorithms. Analyzing Randomized algorithms.

Hiring Problem and Generating Random Permutations.

Randomized Quicksort. Worst-case analysis. Average-case analysis.

Karger’s Min-Cut Algorithm. Faster version by Karger and Stein.

Randomized data structures: Skip Lists, Treaps.

Dynamic Programming: Memoization. Examples of Dynamic Programming: String Matching, BDDs, etc.

Amortized Analysis: Dynamic tables, Aggregate method, Accounting method and Potential method.

Approximate programming.

Competitive Analysis Self-organizing lists Move-to-front heuristic.

Part II

Design of Parallel Algorithms - Parallel Algorithms and Parallel Programming.

Parallel patterns: Map, Reduce, Scan, Mapreduce, Kernel Fusion, etc.

Tools and languages for parallel programming: Posix Threads, OpenMP, Message Passing Interface.

Comparison of Parallel Programing Technologies.

Optimizing and analyzing parallel performance.

Examples of Parallel Algorithms.

• SDG13 - CLIMATE ACTION

Building a faster and better parallel program greatly impacts power consumption reduction. Improving application program efficiency and minimizing the energy intensity by choosing the right technology will affect energy consumption and carbon emissions.

Students are required to have some basic knowledge about data structures and computational complexity.

The assessment of the students is organized according to the schedule provided by the School's Academic Calendar.

The evaluation is based on a written exam focused on:

- The solution of some problems based on the practical application of the course concepts and techniques;

- Open answers to some questions on the course concepts and techniques.

After each written test, the teacher can complement the assessment procedure with an oral examination.

Continuous assessment will be implemented through two intermediate tests: one as a mid-term test and one at the end of the semester. All students are admitted to the second test, regardless of the outcome of the first one. The achieved results will be valid till the end of the academic year or till a student ask to repeat the given part. Each intermediate test contributed to the final grade with 16 points. The exam is considered passed if, in both parts, the students get a grade not less than 7, and the sum of the two grades is greater or equal to 18. 30 cum laude is assigned if students get a sum of grades greater than 30.

If either the first or the second test has a grade less than 7 or the total is less than 18, the student has to take the written test on one of the following dates according to the schedule provided by the School's Academic Calendar. The student may use one of the valid partial results on the next exam dates. In this case, a customized written exam version will be provided to the student for the parts not yet valid.

Participation in innovative-learning classroom activities will be assessed and will contribute to the final evaluation grade. In particular, in case of valid grades, some questions of the written exam could be skipped.

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