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Algorithms II

*Lecturer: Dr F.M. Stajano*

*No. of lectures:* 10

*Prerequisite courses: Algorithms I*

*This course is a prerequisite for Computer Graphics and Image Processing, Complexity Theory, Artificial Intelligence I and II.*

**Aims**

The aim of this course is to give further insights into the design and analysis of non-trivial algorithms through the discussion of several complex algorithms in the fields of graphs and computer graphics, which are increasingly critical for a wide range of applications.

**Lectures**

**Advanced data structures.**Fibonacci heaps. Disjoint sets. [Ref: Ch 20, 21] [2-3 lectures]**Graph algorithms.**Graph representations. Breadth-first and depth-first search. Topological sort. Minimum spanning tree. Kruskal and Prim algorithms. Shortest paths. Bellman-Ford and Dijkstra algorithms. Maximum flow. Ford-Fulkerson method. Matchings in bipartite graphs. [Ref: Ch 22, 23, 24, 25, 26] [5-7 lectures]**Geometric algorithms.**Intersection of segments. Convex hull: Graham's scan, Jarvis's march. [Ref: Ch 33] [1-2 lectures]

**Objectives**

At the end of the course students should

- have a good understanding of how several elaborate algorithms work
- have a good understanding of how a smart choice of data structures may be used to increase the efficiency of particular algorithms
- be able to analyse the space and time efficiency of complex algorithms
- be able to design new algorithms or modify existing ones for new applications and reason about the efficiency of the result

**Recommended reading**

* Cormen, T.H., Leiserson, C.D., Rivest, R.L. & Stein, C. (2001). *Introduction to Algorithms*. MIT Press (2nd ed.). ISBN 0-262-53196-8

Sedgewick, R. (2004). *Algorithms in Java* vol. 2 (note that C and C++ editions are also available and are equally good for this course). Addison-Wesley. ISBN 0-201-36121-3. New edition forthcoming in 2008.

Kleinberg, J. & Tardos, É. (2006). *Algorithm design*. Addison-Wesley. ISBN 0-321-29535-8.

Students are expected to buy and make extensive use of one of the
above textbooks: those not doing so will be severely disadvantaged.
The recommended choice is Cormen *et al.* which covers all
the topics in the syllabus of Algorithms I and II and, in spite of its
quality, is the cheapest. The pointers in the syllabus are to chapters
in that book. The other textbooks are all excellent alternatives and
are sometimes clearer or more detailed than Cormen, but they are not
guaranteed to cover every item in the syllabus. Their relative merits
are discussed in the course handout.

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