Systems and programs are designed for many purposes and in many ways, but it's algorithms that make things work. Good algorithm design requires understanding and modelling an application, and subsequently studying and analysing the computational features of the design. In this course, we study a number of advanced techniques for efficient algorithm design, often at the hand of problems from networks and graphs.
In many applications, networks and graphs are used as a model. Typical examples are networks of roads, or electronic networks. In other applications, the graph model may be less obvious, but appears to be very useful, like for scheduling problems. In this course, we look to the translation of problem to network model, and we look to algorithmic problems and their solutions on networks and graphs.
Some topics are: shortest paths, flow, matchings, stable marriage and stable roommates problems, planar graphs, triangulated graphs, treewidth, graph isomorphism, exact exponential-time algorithms, approximation algorithms, fixed parameter tractability, kernelisation, and some complexity theory.
Course form
Lectures, exercises
Literature
Most literature will be handed out during the course or can be downloaded from the website.
Recommended reading:
- Cormen, Leiserson, Rivest, Stein. Introduction to Algorithms, Third Edition. MIT Press / McGraw-Hill, 2001. ISBN 978-0-262-03384-8.
- Cygan, Fomin, Kowalik, Lokshtanov, Marx, Pilipczuk, Pilipczuk, Saurabh. Parameterized Algorithms. Springer, 2015. ISBN 978-3-319-21274-6.
- Fomin and Kratsch. Exact Exponential Algorithms. Springer, 2010. ISBN 978-3-642-16532-0.
- Ausiello, Crescenzi, Gambosi, Kann, Marchetti Spaccamela, Protasi. Complexity and Approximation. Springer, 1998. ISBN 978-3-540-65431-5.
- Kleinberg and Tardos. Algorithm Design. Pearson / Addision Wesley, 2005. ISBN 978-0-321-29535-4.
- Ahuja, Magnanti, Orlin. Network Flows. Pearson, 1993. ISBN-13: 978-0-136-17549-0.
- Schrijver. Combinatorial Optimization. Polyhedra and Efficiency. Springer, 2003. ISBN 978-3-540-44389-6.
Note that these books are not obligatory. Participation in classes is recommended: much is not covered in the books !
|