Efficient Algorithms (MAE748)

Undergraduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE748
Semester	7
Course Title	Efficient Algorithms
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The course is introducing advanced algorithmic concepts and techniques. Several optimization problems are examined and solved using algorithmic techniques. Upon a successful completion of the course, the student will be able to: apply advanced algorithmic techniques and methods to solve advanced optimization problems, understand and apply advanced algorithmic analysis methods to study the efficiency of algorithms, analyze and compare the effectiveness of different algorithmic methods, combine advanced algorithmic techniques to solve new problems.

General Competences

Search for, analysis and synthesis of data and information, with the use of the necessary technology Adapting to new situations Criticism and self-criticism Production of free, creative and inductive thinking

Syllabus

Basics: Algorithm analysis (correctness, time and space complexity), asymptotic analysis (worst and average care), recursive algorithms (Strassen’s algorithm for the matrix multiplication problem), lower bounds (comparison-based sorting, the convex-hull problem). Amortized analysis: The accounting, aggregate and potential methods. Minimum spanning trees: The greedy algorithms by Tarjan, Prin and Kruskal. Minimum cuts: The algorithm by Stoer and Wagner. Maximum flows: Basis terminology (flow network, augmenting path, residual network) the max-flow min-cut theorem, the algorithms by Ford και Fulkerson, Edmonds και Karp, and Dinitz. Planar graphs: Basic terns, Euler’s formula, Kurantowski Theorem, the 5-color theorem, drawings of planar graphs: the algorithm by de Fraysseix, Pach and Pollack, the crossing Lemma. Approximation algorithms: simple algorithms of constant approximation factor, Christofides’ algorithm for the traveling salesman problem, approximation schemes for knapsack and bin packing. Randomized algorithms: simple randomized algorithms for verifying polynomial identities and 2-SAT, random walks.

Teaching and Learning Methods - Evaluation

Delivery	Face to face
Use of Information and Communications Technology	Yes
Teaching Methods	Activity Semester Workload Lectures 39 Self study 78 Exercises 33 Course total 150
Student Performance Evaluation	Written final exam. Two exercises.

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

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