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Department of Computer Science and Technology

Undergraduate

Course pages 2021–22

Algorithms 2

Principal lecturer: Dr Damon Wischik
Taken by: Part IA CST
Hours: 12
Format: Video lectures and in-person Q&A sessions
Suggested hours of supervisions: 3
Prerequisites: Algorithms 1
This course is a prerequisite for: Artificial Intelligence, Complexity Theory, Prolog, Randomised Algorithms
Past exam questions

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.