12:30-2:00 PM, Thu 12:30-2:00 PM. All lectures in HH/102 (but first meeting Tue 5/9 in ITB/222)
Textbook: "Introduction to Algorithms",
3rd Ed., by T. Cormen, C. Leiserson, R. Rivest, and C. Stein.
- More information about the expansion of matroids to greedoids can be found
in the references of the Wikipedia article here.
Especially interesting are the articles by Björner &
Ziegler, and Helman et al.
- A very nice recent survey on Max Flow here.
The course will cover data structures and algorithms topics at
a graduate level. This means that this
course will not be a
repetition of an undergraduate course on the subject, such as,
e.g., CAS CS 2C03, but it will rather cover more advanced
topics, or known material at a more advanced /deeper level of
understanding. For example, Kruskal's algorithm for the
minimum spanning tree problem should already be known, but we
will examine it under a general framework for greedy
algorithms called matroid theory. Therefore it is assumed that
the students already know the material of Chapters 1-5
(Foundations) of the text (note:
students who are not familiar with this material must
cover it as soon as possible).
A tentative list of topics we will try to cover follows.
- Binomial heaps, an example of worst-case analysis
- Amortized analysis (Ch. 17)
- Fibonacci heaps, an example of amortized analysis
- Hash tables, an example of randomized analysis (Ch.
- Greedy algorithms and matroids (Ch. 16)
- Dynamic programming and all-pairs shortest paths (Ch.
- Maximum flow (Ch. 26)
- Linear Programming and Duality (Ch. 29)
- Primal-Dual schema as an algorithmic design tool
- NP-completeness (Ch. 34)
- Approximation algorithms (Ch. 35)
40% Midterm exam (Tue
24/10, 6:30-9:00 pm, Rm. ABB/136, open book + notes)
60% Final exam
McMaster Course Policies
- Problem set #1:
Do Exer. 5.2-1 - 5.2-5, 5.4-6, 17.1-3, 17.2-2, 17.3-2,
Prob. 17.2.b, Exer. 19.3-1, 19.4-2 (due during lecture 5/10)
- Problem set #2: Do
Exer. 11.1-4, 11.2-5, 11.4-5, 16.2-1 - 16.2-3, 16.4-3,
16.4-5, 16.5-2. Is Dijkstra's algorithm an application of
GREEDY (p. 440)? (i.e., is there a corresponding matroid?)
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