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Lecture Contents

CLR2 refers to the second edition of the textbook by Cormen, Leiserson and Rivest (2001)
CLR1 refers to the first edition of the same book (1990)
NN refers to the textbook by Neapolitan and Naimipour.

Tentative schedule (it will be updated if changes occur):
days and tasks Lecture Contents:textbook
Sep 06
Sep 10
Sep 13
Sep 17
Sep 20
Introduction to the course.
Introduction to the theory of NP completeness.
Turing machines and the RAM model.
Review of formal languages.
Polynomial time and the class P.
Polynomial time verification and the class NP.
my notes (pdf,ps)
CLR2 34.1, 34.2 (CLR1 36.1,36.2)
Sep 24
Sep 27
NP-completeness and reducibility.
CLR2 34.3 (CLR1 36.3)
Oct 01 (A1 out)
Oct 04
NP-completeness proofs (SAT and 3-CNF).
NP-complete problems: subset-sum
CLR2 34.4 (CLR1 36.4)
CLR2 34.5.5 (CLR1 36.5.3 different!)
Oct 08 thanksgiving holiday-
Oct 11NP-complete problems: clique and vertex cover. CLR2 34.5.1,34.5.2 (CLR1 36.5.1,36.5.2)
Oct 15NP-complete problems: hamiltonian cycle and TSP.CLR2 34.5.3 (CLR1 36.5.4 different!)
CLR2 34.5.4 (CLR1 36.5.5)
Oct 18 (A1 in)Approximation algorithms.
An approximation algorithm for the vertex-cover.
CLR2 intro35, 35.1 (CLR1 intro37,37.1)
Oct 22Midterm Test Review-
Oct 29 (A2 out)An approximation algorithm for the
TSP with triangle inequality,
non-approximabiblity for general TSP
CLR2 35.2 (CLR1 37.2)
Nov 01An approximation algorithm for
the set-covering problem.
CLR2 35.3 (CLR1 37.3)
Nov 05An approximation algorithm for the weighted
vertex cover using linear programming
CLR2 35.4 (not in CLR1)
Nov 08
Nov 12
The backtracking approach and the n queens.
Backtracking for the subset-sum
NN 5.1, 5.2, 5.4
Nov 15 (A2 in, A3 out)
Nov 19
Backtracking for graph colouring, hamiltonian path, knapsack.NN 5.5, 5.6, 5.7
Nov 22
Nov 26
The branch-and-bound (B&B) technique
(breadth-first and best-first).
B&B for the 0-1 knapsack.
NN 6.1
Nov 29 (A3 in)B&B for the TSPNN 6.2
Dec 01Final Review.-
Background references:textbook sections
Basic notions: Sets, relations, functions, graphs
Growth of functions
Representations of graphs
CLR2 App.B (CLR1 5)
CLR2 3 (CLR1 2)
CLR2 22.1 (CLR1 23.1)