Algorithms, Data Structures and Databases

Credits
6
Types
Elective
Requirements
This subject has not requirements , but it has got previous capacities
Department
CS;ESSI
Web
https://learnsql.fib.upc.es/moodle/
This is a fundamental course that covers basic concepts on algorithms, data structures and databases. This course spans two different tracks: one for students who have a major in Computer Science and another track for the rest.
During the first weeks, the course is different for both tracks. For the former, it introduces students to CS-specific advanced topics for Data Science, while for the latter it requires the students to cover basic material on algorithms, data structures and databases in a guided, yet autonomous learning manner.

The last part of the course (corresponding to the last 5 weeks) is common and it is structured as project-based learning. A statement about an end-to-end Data Science project will be delivered and students will need to create the required software infrastructure, using adequate tools.

The objective is to help students get a rigorous and strong knowledge required by the following master courses (for students with a minor in CS) or investigate further CS-specific topics for Data Science (for students with a major in CS). Last, but not least, the course promotes adopting good habits when creating software projects for Data Science in the final project.

Weekly hours

Theory
1
Problems
0
Laboratory
2.9
Guided learning
0
Autonomous learning
6.85

Objectives

  1. To analyse the cost of iterative and recursive algorithms
    Related competences: CG1, CB9, CTR4, CTR6,
    Subcompetences
    • Compare the efficiency of different algorithms for solving the same problem and select the most appropriate one.
    • Understand the definitions of the Big-O, Omega and Theta asymptotic notations and their usefulness in characterising the efficiency of algorithms in time and space.
    • Compute the cost of an algorithm in the worst, best and average cases.
  2. To review some simple data structures: stacks, queues, lists, and trees
    Related competences: CG1, CB9, CTR4, CTR6,
  3. To know, explain, design, analyse, compare and implement the main data structures and algorithms that can be used to implement priority queues
    Related competences: CG1, CB9, CTR4, CTR6,
  4. To know, explain, design, analyse, compare and implement the main data structures and algorithms that can be used to implement dictionaries
    Related competences: CG1, CB9, CTR4, CTR6,
  5. To know, explain, design, analyse, compare and implement the main data structures and algorithms that can be used to represent graphs and solve classic graph problems such as traversals, topological ordering and shortest paths
    Related competences: CG1, CB9, CTR4, CTR6,
  6. To know, understand, explain, analyse and compare some algorithm design techniques: greedy, divide and conquer, and dynamic programming
    Related competences: CG1, CB9, CTR4, CTR6,
  7. To be aware of the limits of computation: to understand the definitions of the P and NP classes, the concept of Polynomial-Time reduction, the notion of NP-Completeness, and to know some classic NP-complete problems
    Related competences: CG1, CB9, CTR4, CTR6,
  8. Describe what is a database and a database management system
    Related competences: CG1, CB9, CTR4, CTR6,
    Subcompetences
    • Enumerate the objectives of a database management system
    • Distinguish the objectives of a database management system from a file system
    • Enumerate the objectives of a database management system
    • Distinguish the objectives of a database management system from a file system
  9. Effectively use the standard Structured Query Language (SQL) to query relational databases
    Related competences: CG1, CB9, CTR4, CTR6,
  10. Explain the relational data model, including its data structures, the relational algebra and integrity constraints
    Related competences: CG1, CB9, CTR4, CTR6,
    Subcompetences
    • Express any SQL query in terms of a relational algebra expression
    • Express any SQL query in terms of a relational algebra expression
  11. Given a set of informational requirements, model the logic schema of a relational database
    Related competences: CG1, CB9, CTR4, CTR6,
  12. Identify the main objectives of a database management system query optimizer
    Related competences: CG1, CB9, CTR4, CTR6,
    Subcompetences
    • Explain what is a cost model and how to automatically generate physical access plans
    • Evaluate the main pros and cons of the most popular data structures used by database management systems given a workload characterized in terms of database cardinality, size and the operations expected and their selectivity factor
    • Evaluate the main pros and cons of the most popular data structures used by database management systems given a workload characterized in terms of database cardinality, size and the operations expected and their selectivity factor
    • Explain what is a cost model and how to automatically generate physical access plans
  13. Develop a quality realistic end-to-end system architecture for a data science project
    Related competences: CG1, CG2, CB9, CTR3, CTR4, CTR6,

Contents

  1. Basics of Analysis of Algorithms
    Worst case, best case and average case cost analysis. Asymptotic order of growth notations: Big-O, Omega and Theta. Analysis of the cost of iterative and recursive algorithms.
  2. Simple Data Structures: Review
    Stacks, queues, lists and trees.
  3. Priority Queues
    Operations of priority queues. Implementations with heaps. Heapsort.
  4. Dictionaries
    Operations of dictionaries. Basic implementations: tables and lists. Advanced implementations: hash tables, binary search trees, and AVL trees.
  5. Graphs
    Representations: adjacency matrices, adjacency lists and implicit representations. Depth-first search (DFS). Breadth-first search (BFS). Topological sort. Algorithms for shortest paths. Algorithm for minimum spanning trees.
  6. Algorithm design techniques
    Greedy, divide and conquer, and dynamic programming.
  7. Introduction to NP and Computational Intractability
    Basic introduction to P and NP classes, Polynomial-Time reduction, and NP-completeness. Examples of classic NP-complete problems.
  8. Introduction to databases and database management systems
    Main concepts on databases and database management systems. Relational database management systems.
  9. SQL: Data-definition language and data-manipulation language
    Introduction to the SQL language
  10. The relational model
    Data structures and integrity constraints. Views.
  11. The relational algebra
    The relational algebra operators and how to build data pipes with them. Notion of semantic and syntactic optimization.
  12. Logical design of relational databases
    Normalization theory. Translating conceptual schemas into relational schemas.
  13. Notions of physical design and physical database optimization
    Notions of query optimizer, access plan and cost model
  14. Data Science-related advanced topics
    Students with a major in Computer Science will investigate on advanced topics specific for data science projects. For example, data quality, entity resolution, data integration, etc.

Activities

Activity Evaluation act


Basics of Analysis of Algorithms

To compare the efficiency of different algorithms for solving the same problem and select the most appropriate one. To compute the cost of an algorithm in the worst, best and average cases. To understand the definitions of the asymptotic order of growth notations Big-O, Omega and Theta, and their usefulness in characterising algorithm efficiency in time and space.
Objectives: 1
Contents:
Theory
1h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
0h

Review of simple data structures

Operations. Lists, Stacks, Queues, Trees
Objectives: 2
Contents:
Theory
1h
Problems
0h
Laboratory
3h
Guided learning
0h
Autonomous learning
0h

Priority Queues

Operations of priority queues. Implementations with heaps. Heapsort.
Objectives: 3
Contents:
Theory
1h
Problems
0h
Laboratory
3h
Guided learning
0h
Autonomous learning
0h

Dictionaries

Operations of dictionaries and ordered dictionaries. Basic implementations: tables and lists. Advanced implementations: hash tables, binary search trees, AVL trees
Objectives: 4
Contents:
Theory
1h
Problems
0h
Laboratory
3h
Guided learning
0h
Autonomous learning
0h

Graphs

Representations: adjacency matrices, adjacency lists and implicit representation. Depth-first search (DFS). Breadth-first search (BFS). Topological sort. Dijkstra's algorithm for shortest paths. Prim's algorithm for minimum spanning trees.
Objectives: 5
Contents:
Theory
1h
Problems
0h
Laboratory
3h
Guided learning
0h
Autonomous learning
0h

Algorithmic schemes

Divide and conquer, Greedy algorithms, Dynamic Programming, Exhaustive search, Backtracking.
Objectives: 6
Contents:
Theory
1h
Problems
0h
Laboratory
4h
Guided learning
0h
Autonomous learning
0h

Notions of Intractability

Basic introduction to P and NP classes. NP-completeness.
Objectives: 7
Contents:
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

Partial Exam

For students with a minor in Computer Science, this exams evaluates their knowledge on fundamental concepts of algorithms, data structures and databases
Objectives: 1 2 4 5 6 7 3
Week: 12
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

Introduction to databases and database management systems

The student attends the lecture, takes notes and participates in the session exercises
Objectives: 8
Contents:
Theory
1h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

SQL

The student attends the lecture, takes notes and participates in the session exercises
Objectives: 9
Contents:
Theory
0h
Problems
0h
Laboratory
3h
Guided learning
0h
Autonomous learning
0h

The Relational Model

The student attends the lecture, takes notes and participates in the session exercises
Objectives: 10 11
Contents:
Theory
1h
Problems
0h
Laboratory
2h
Guided learning
0h
Autonomous learning
0h

Logical Design of Relational Databases

The student attends the lecture, takes notes and participates in the session exercises
Objectives: 10 11
Contents:
Theory
1h
Problems
0h
Laboratory
3h
Guided learning
0h
Autonomous learning
0h

Physical Optimization

The student attends the lecture, takes notes and participates in the session exercises
Objectives: 12
Contents:
Theory
3h
Problems
0h
Laboratory
4h
Guided learning
0h
Autonomous learning
0h

Final Exam

For students with a minor in Computer Science, this exams evaluates their knowledge on fundamental concepts of algorithms, data structures and databases
Objectives: 8 9 10 11 13 12
Week: 17
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

Data Science Advanced Topics project (DS-AT project)

Students with a major in Computer Science will investigate on advanced topics specific for data science projects. For example, data quality, entity resolution, data integration, etc. Students with a minor in Computer Science will investigate and further study the fundamental concepts introduced in the lecturing hours.

Theory
0h
Problems
0h
Laboratory
4h
Guided learning
0h
Autonomous learning
40h

Data Science End-to-End Project (DS-EE)

All students will undertake a project spanning all main phases of a data science. As result, they are asked to develop a quality realistic end-to-end system architecture for a data science project.

Theory
0h
Problems
0h
Laboratory
4h
Guided learning
0h
Autonomous learning
45h

Teaching methodology

During the first 10 weeks, the students are divided in two tracks: one for students with a minor in computer science (track 1) and another one for students with a major in computer science (track 2).

Students in track 1 will study fundamental concepts in algorithms, data structures and databases. First, additional material to read, study and understand is provided. Students will have a large bank of exercises to practice their understanding on their own. Then, in the face-to-face lectures, the lecturer will solve doubts and go through representative exercises to guarantee a solid understanding. Also, for the most complex concepts, some regular teaching sessions will be scheduled.

Students in track2 will undertake a research project related to advanced topics of algorithms, data structures and databases within the context of data science. Relevant and critical problems such as data integration, entity resolution and data quality will be proposed. The student will have access to a description of the problem, some seminal research papers and reference tools in this matter.

The last 5 weeks of the semester is common for all students regardless of the track they followed during the first 10 weeks. During these weeks the course project takes place. Students must create a end-to-end system architecture to ingest, store, process, learn models and deploy such system for a realistic project with realistic data.

This course has a strong self-learning component. Complementing it, the lecturers will provide additional material, advice hours and complementary lectures and labs to guarantee a solid comprehension.

Evaluation methodology

Let E1 be the score of the partial exam,
E2 the score of the final exam,
RPM the score of the DS-AT project and
CPM the score of the DS-EE project.

Then,

NE = MAX(E2, E1)
If the student followed track 1 (see methodology) then NT = NE
else if student followed track 2 (see methodology) then NT = RPM

The final mark will be 0.6*NT + 0.4*CPM
Transversal competences will weight a 0% in the final score.

Bibliography

Basic

Complementary

Web links

Previous capacities

This course assumes basic competences in algorithms, data structures and databases. The course is structured to cope with different backgrounds and learning needs but basic knowledge on Computer Science principles is assumed: notions of computer architecture, basic programming constructs and data structures.