Tentative schedule (it will be updated if changes occur):
|das and tasks||Lecture Contents:||textbook
Sep 18 (A1 out)
|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)
|NP-completeness and reducibility.
CIRCUIT-SAT is NP-hard.
|CLR2 34.3 (CLR1 36.3)|
|Sep 29 (A1-A in)
|NP-completeness proofs : SAT and 3-CNF.||CLR2 34.4 (CLR1 36.4)|
|Oct 06||NP-complete problems: clique and vertex cover.||CLR2 34.5.1,34.5.2 (CLR1 36.5.1,36.5.2)|
|Oct 09 (A1-B in)||NP-complete problems: TSP.||CLR2 34.5.4 (CLR1 36.5.5)|
|Oct 13||thanksgiving holiday||-|
|Oct 16||NP-complete problems: hamiltonian cycle||CLR2 34.5.3 (CLR1 36.5.4 different!)|
|Oct 20||Midterm Test Review||-|
|Oct 23 (A2 out)||MIDTERM TEST||-|
|Oct 27||Approximation algorithms.
An approximation algorithm for the vertex-cover.
|CLR2 intro35, 35.1 (CLR1 intro37,37.1)|
|Oct 30||An approximation algorithm for the
TSP with triangle inequality.
|CLR2 35.2 (CLR1 37.2)|
|Nov 03||Non-approximabiblity for general TSP||CLR2 35.2 (CLR1 37.2)|
|Nov 06||Midterm Test Solution||-|
Nov 13 (A2 in/ A3 out)
|An approximation algorithm for the set-covering problem.
Course evaluation questionaire.
|CLR2 35.3 (CLR1 37.3)|
|Nov 17||An approximation algorithm for the weighted
vertex cover using linear programming
|CLR2 35.4 (not in CLR1)|
|Nov 20||The backtracking approach and the n queens.||NN 5.1, 5.2|
|Nov 24||Backtracking for graph colouring, hamiltonian path.||NN 5.5, 5.6, 5.7|
|Nov 27 (A3 in)
|All or less topics of (TBA later):
The branch-and-bound (B&B) technique
(breadth-first and best-first).
B&B for the 0-1 knapsack.
|NN 6.1, 6.2|
|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)