Algorithms 2

Aims

The aim of this course is to provide an introduction to computer algorithms and data structures, with an emphasis on foundational material.

Lectures

• Graph algorithms. Graph representations. Breadth-first and depth-first search. Topological sort. Minimum spanning tree. Kruskal and Prim algorithms. Single-source shortest paths: Bellman-Ford and Dijkstra algorithms. All-pairs shortest paths: matrix multiplication and Johnson’s algorithms. Maximum flow: Ford-Fulkerson method, Max-Flow Min-Cut Theorem. Matchings in bipartite graphs. [Ref: CLRS3 chapters 22, 23, 24, 25, 26] [about 7 lectures]
• Advanced data structures. Binomial heap. Amortized analysis: aggregate analysis, potential method. Fibonacci heaps. Disjoint sets. [Ref: CLRS3 chapters 17, 19, 20, 21] [about 4 lectures]
• Geometric algorithms. Intersection of segments. Convex hull: Graham’s scan, Jarvis’s march. [Ref: CLRS3 chapter 33] [about 1 lecture]

Objectives

At the end of the course students should:

• have a thorough understanding of several classical algorithms and data structures;
• be able to analyse the space and time efficiency of most algorithms;
• 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 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. and Stein, C. (2009). Introduction to Algorithms. MIT Press (3rd ed.). ISBN 978-0-262-53305-8

Sedgewick, R., Wayne, K. (2011). Algorithms. Addison-Wesley. ISBN 978-0-321-57351-3.

Kleinberg, J. and Tardos, É. (2006). Algorithm design. Addison-Wesley. ISBN 978-0-321-29535-4.

Knuth, D.A. (2011). The Art of Computer Programming. Addison-Wesley. ISBN 978-0-321-75104-1.