Computer Science 690
Probabilistic Analysis of Algorithms and Data Structures
May 25, 2024

Fall 2024 --- Course Syllabus


Luc Devroye | Email | McConnell Engineering Building, Room 300N | Live office hours, TBA.

Location and time  

Monday and Wednesday, 8:30--10am. Lectures start on Wednesday, August 28, 2024 and run until Wednesday, December 4, 2024. No lectures on October 14 and 16 (reading break). There won't be any lectures on Monday, September 2 (Labour Day),

We meet in McConnell 321 (the lounge). Course notes will be handed out in class.

Teaching Assistant

Caelan Atamanchuk, McConnell Engineering 310/311. Email Caelan. Office hours: TBA.


This course looks at basic methods for analyzing the average behavior of algorithms and data structures. It is shown how conventional and modern probability theoretical techniques can be used in this respect. The list of topics does not pretend to be exhaustive; rather, it is selected to give a broad horizontal view of possible applications. The students should be familiar with elementary concepts in probability theory and data structures.


Binary search trees Connection with the theory of records and random permutations.
Analysis of depth and height.
Quadtrees, k-d trees, union-find trees.
The uniform random recursive tree.
Preferential attachment trees.
Introduction to branching processes, branching random walks.
Conditional branching processes Analysis of simple families of random trees.
Galton-Watson trees.
Random graphs Simple random graph models, independent sets, coloring.
The second moment method.
Analysis of simple heuristics for graph problems.
The Erdös-Rényi theorem on connected graphs.
Random geometric graphs, the Gilbert disc model, percolation.
Randomized algorithms Introduction to the methodology.
Finding the k-th largest quickly on the average.
Randomized routing on networks.
Exponential large deviation inequalities.
Closest point problems.
Random incremental algorithms.
Randomzed approximation algorithms.
Combinatorial search problems Euclidean traveling salesman problem.
Assignment problems.
Martingales and the bounded differences method.
Concentration inequalities.
Markov chains Basic properties.
Markov chain Monte Carlo.
Generating random combinatorial objects.
Rapid mixing. Mixing time.
Entropy Entropy, coding and compression.
Entropy and random tries.
Digital search trees.


About nine sets of theoretical problems will be assigned.


There is no specific textbook. Course notes will be handed out.

Selected references  

Some references are given below.

N. Alon, J. Spencer, and P. Erdös, The Probabilistic Method, John Wiley, New York, 1992.

B. Bollobas, Random Graphs, Academic Press, New York, 1985.

L. Devroye, "Branching processes in the analysis of the heights of trees," Acta Informatica, vol. 24, pp. 277--298, 1987.

L. Devroye, "Applications of the theory of records in the study of random trees," Acta Informatica, vol. 26, pp. 123--130, 1988.

S. Janson, T. Luczak, A. Rucinski, Random Graphs, Wiley-Interscience, New York, 2000.

R. M. Karp, "The probabilistic analysis of some combinatorial search algorithms," in: Algorithms and Complexity, ed. J. F. Traub, pp. 1--19, Academic Press, New York, 1976.

R. M. Karp and J. M. Steele, "Probabilistic analysis of heuristics," in: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, ed. E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan and D. B. Shmoys, pp. 181--205, John Wiley, New York, 1985.

D. E. Knuth, The Art of Computer Programming, Vol. 3 : Sorting and Searching, Addison-Wesley, Reading, Mass, 1973.

H. M. Mahmoud, Evolution of Random Search Trees, John Wiley, New York, 1992.

R. Motwani and P. Raghavan, Randomized Algorithms, Cambridge University Press, 1995.

E. M. Palmer, Graphical Evolution, John Wiley, New York, 1985.

J. Pearl, Heuristics. Intelligent Search Strategies for Computer Problem Solving (Chapter 5), Addison-Wesley, Reading, Mass, 1984.

W. Szpankowski, Average Case Analysis of Algorithms on Sequences, Springer-Verlag, New York, 2001.

J. S. Vitter and P. Flajolet, "Average-case analysis of algorithms and data structures," in: Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity, ed. J. van Leeuwen, pp. 431--524, MIT Press, Amsterdam, 1990.