Design and Analysis of Algorithms

This core course covers good principles of algorithm design, elementary analysis of algorithms, and fundamental data structures. The emphasis is on choosing appropriate data structures and designing correct and efficient algorithms to operate on these data structures.

This is a first course in data structures and algorithm design. Students will:

• learn good principles of algorithm design;
• learn how to analyse algorithms and estimate their worst-case and average-case behaviour (in easy cases);
• become familiar with fundamental data structures and with the manner in which these data structures can best be implemented; become accustomed to the description of algorithms in both functional and procedural styles;
• learn how to apply their theoretical knowledge in practice (via the practical component of the course).

• Program costs: time and space. Worst case and average case analysis. Asymptotics and "big O" notation. Polynomial and exponential growth. Asymptotic estimates of costs for simple algorithms. Use of induction and generating functions. [2]
• Data structures and their representations: arrays, lists, stacks, queues, trees, heaps, priority queues, graphs. [3]
• Algorithm design strategies: top down design, divide and conquer. Application to sorting and searching and to matrix algorithms. Solution of relevant recurrence relations. [4]
• Graph algorithms: examples of depth-first and breadth-first search algorithms. Topological sorting, connected components. [3]
• Introduction to discrete optimisation algorithms: dynamic programming, greedy algorithms, shortest path problems. [2]
• Linear sorting and comparator networks (if time).

Basic strategies of algorithm design: top-down design, divide and conquer, average and worst-case criteria, asymptotic costs. Simple recurrence relations for asymptotic costs. Choice of appropriate data structures: arrays, lists, stacks, queues, trees, heaps, priority queues, graphs, hash tables. Applications to sorting and searching, matrix algorithms, shortest-path and spanning tree problems. Introduction to discrete optimisation algorithms: dynamic programming, greedy algorithms. Graph algorithms: depth first and breadth first search.

• T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein. Introduction to Algorithms, 2nd edition, MIT Press, 2001 (or the 1st edition, published in 1990).
• M. T. Goodrich and R. Tommassia. Algorithm Design, Wiley, 2002.
• S. Dasgupta, C. Papadimitriou, and U. Vazirani. Algorithms. McGraw-Hill Higher Education. 2006