Additional information: https://moodle.fct.unl.pt/course/view.php?id=4941
Study of efficient algorithms for solving fundamental graph problems.
Use of three algorithm design techniques (greedy strategies, dynamic programming and transform-and-conquer).
Understanding of the basic concepts of the Theory of Complexity.
Knowledge
Define and identify three algorithm design techniques: greedy strategies, dynamic programming and transform-and-conquer.
Know the fundamental graph algorithms, the required abstract data types and the data structures used to implement them efficiently.
Understand amortized analysis.
Define some complexity classes and understand some open problems.
Application
Design and analyse a dynamic programming algorithm.
Formulate a clean graph problem from a real-world problem and adapt a classical algorithm to solve it.
Choose, compare, adapt, and use suitable data structures for a given problem.
Calculate the running time of an algorithm based on the amortized running times of the inner functions and perform their amortized analysis.
Evaluate solutions and justify choices.
Make NP-complete proofs.
(1) Dynamic programming.
(2) Introduction to the study of graphs. Fundamental definitions. The abstract data types undirected graph and directed graph. Implementations of graphs.
(3) Elementary graph algorithms. Depth-first and breadth-first traversals. Topological sorting.
(4) Minimum spanning trees. Kruskal’s algorithm. The disjoint sets abstract data type.
(5) Amortized analysis. The potential method.
(6) Prim’s algorithm. The adaptable priority queue abstract data type.
(7) Shortest paths. The algorithms of Dijkstra, Bellman-Ford, and Floyd-Warshall.
(8) Flow networks. Maximum flows. The Ford-Fulkerson method. The Edmonds-Karp algorithm. Maximum bipartite matchings. Minimum cuts.
(9) Introduction to the Theory of Complexity. The classes P, NP, PSPACE, and EXPTIME. The suffixes hard and complete. Problem reductions. Some open problems.
Main References
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms (3rd edition). The MIT Press, 2009.
Jon Kleinberg and Éva Tardos. Algorithm Design. Addison-Wesley, 2005.
Complementary References
Anany Levitin. Introduction to The Design and Analysis of Algorithms (3rd edition). Addison-Wesley, 2011
Michael R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, 1979.
Steven S. Skiena. The Algorithm Design Manual (2nd edition). Springer, 2008.
Steven S. Skiena and Miguel A. Revilla. Programming Challenges: The Programming Contest Training Manual. Springer, 2003.
Students should:
(a) be proficient in object-oriented programming;
(b) be familiar with the fundamental data structures (linked lists, hash tables, binary search trees, binary heaps);
(c) be able to calculate the time and the space complexities of algorithms.
Hours per credit | 28 | ||
Hours per week | Weeks | Hours | |
Aulas práticas e laboratoriais | 26.0 | ||
Aulas teóricas | 39.0 | ||
Avaliação | 5.0 | ||
Self study | 60.0 | ||
Others | 2.0 | ||
Project | 36.0 | ||
Total hours | 168 | ||
ECTS | 6.0 |